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Chapter 14 Probability - Assertion Reason | Akash Maths
← Assertion-Reason Chapters
✦ NCF 2023 ALIGNED • CBSE CLASS X ✦

Chapter 14: Probability

Assertion-Reason Question Bank

✨ Explore more at: www.akashmaths.online

Standard CBSE Options Framework

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Q1Assertion-Reason
Assertion (A)
When \(3\) coins are tossed, probability of getting all heads is \(\frac{1}{4}\).
Reason (R)
Sample space for \(3\) coins has \(2^3 = 8\) outcomes \(\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}\), so \(P(HHH) = \frac{1}{8}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (it is \(1/8\), not \(1/4\)). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q2Assertion-Reason
Assertion (A)
In a simultaneous throw of two coins, probability of getting \(2\) heads is \(\frac{1}{4}\).
Reason (R)
Sample space for tossing two coins has \(2\) outcomes.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(\{HH\}\) out of \(4\)). Reason (R) is false because sample space has \(2^2 = 4\) outcomes, not \(2\).
Correct Answer: (C)

Assertion true; Reason false.
Q3Assertion-Reason
Assertion (A)
If a die is thrown, probability of getting a number less than \(7\) is \(0\).
Reason (R)
Getting a number less than \(7\) on a die is a sure event, so its probability is \(1\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (it is a sure event with probability \(1\)). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q4Assertion-Reason
Assertion (A)
If odds against an event are \(2:3\), then its probability is \(\frac{2}{5}\).
Reason (R)
If odds against event \(E\) are \(a:b\), then \(P(E) = \frac{b}{a+b} = \frac{3}{2+3} = \frac{3}{5}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (probability is \(3/5\), not \(2/5\)). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q5Assertion-Reason
Assertion (A)
The probability of getting a prime number on rolling a single fair die is \(\frac{1}{2}\).
Reason (R)
Prime numbers on a die are \(2, 3, 5\), total \(3\) outcomes out of \(6\), so \(P = \frac{3}{6} = \frac{1}{2}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

Prime numbers \(\{2, 3, 5\}\), \(P = 3/6 = 1/2\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q6Assertion-Reason
Assertion (A)
The probability of getting an even number on rolling a die is \(\frac{1}{2}\).
Reason (R)
Even numbers on a die are \(2, 4, 6\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true.
Correct Answer: (B)

Both true.
Q7Assertion-Reason
Assertion (A)
The sum of probabilities of complementary events is \(0\).
Reason (R)
For any event \(E\), \(P(E) + P(\bar{E}) = 1\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (sum is \(1\)). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q8Assertion-Reason
Assertion (A)
The probability of selecting a red face card from a deck of \(52\) cards is \(\frac{3}{26}\).
Reason (R)
There are \(6\) red face cards (\(3\) of Hearts, \(3\) of Diamonds) in a deck of \(52\) cards, so \(P = \frac{6}{52} = \frac{3}{26}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

Red face cards \(= 6\). \(P = 6/52 = 3/26\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q9Assertion-Reason
Assertion (A)
The probability of an impossible event is \(0\).
Reason (R)
An impossible event has no favorable outcomes in the sample space \(S\), so \(n(E) = 0 \implies P(E) = \frac{0}{n(S)} = 0\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

\(P(E) = n(E)/n(S) = 0/n(S) = 0\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q10Assertion-Reason
Assertion (A)
The probability of drawing a black card or a king from a deck is \(\frac{28}{52} = \frac{7}{13}\), but if calculated as \(26 + 4 = 30\), it gives \(\frac{30}{52}\).
Reason (R)
Black cards include \(2\) black kings, so adding \(26 + 4\) double counts \(2\) black kings. Favorable cards \(= 26 + 2 = 28 \implies P = \frac{28}{52} = \frac{7}{13}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) claims \(\frac{30}{52}\) without correction is correct, which is false. Reason (R) gives the true double-counting correction.
Correct Answer: (D)

Assertion false; Reason true.
Q11Assertion-Reason
Assertion (A)
Probability of drawing a red card from deck of \(52\) cards is \(\frac{1}{2}\).
Reason (R)
There are \(13\) red cards in a deck.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(26/52 = 1/2\)). Reason (R) is false because there are \(26\) red cards (\(13\) Hearts \(+\) \(13\) Diamonds), not \(13\).
Correct Answer: (C)

Assertion true; Reason false.
Q12Assertion-Reason
Assertion (A)
The probability of a non-leap year having \(53\) Sundays is \(\frac{2}{7}\).
Reason (R)
A non-leap year has \(365\) days \(= 52\) weeks \(+ 1\) extra day, so probability of \(53\) Sundays is \(\frac{1}{7}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (it is \(1/7\), \(2/7\) is for leap year). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q13Assertion-Reason
Assertion (A)
The probability of getting at least one head when two unbiased coins are tossed is \(\frac{3}{4}\).
Reason (R)
Sample space \(S = \{HH, HT, TH, TT\}\), \(n(S) = 4\). Favorable outcomes for 'at least one head' are \(\{HH, HT, TH\}\), \(n(E) = 3 \implies P = \frac{3}{4}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

Favorable outcomes \(= 3\), total \(= 4\), \(P = 3/4\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q14Assertion-Reason
Assertion (A)
Probability of a leap year having \(53\) Sundays is \(\frac{2}{7}\).
Reason (R)
A leap year has \(366\) days, which is \(52\) weeks and \(1\) extra day.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(366\) days \(= 52\) weeks \(+ 2\) extra days, \(P = 2/7\)). Reason (R) is false because a leap year has \(2\) extra days, not \(1\) extra day.
Correct Answer: (C)

Assertion true; Reason false.
Q15Assertion-Reason
Assertion (A)
The probability of getting a total of \(13\) when two dice are thrown is \(0\).
Reason (R)
Maximum possible sum on throwing two dice is \(6 + 6 = 12\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true facts about two dice.
Correct Answer: (B)

Both true.
Q16Assertion-Reason
Assertion (A)
The probability of getting a number greater than \(6\) when a single die is rolled is \(0\).
Reason (R)
A standard die has faces numbered \(1\) to \(6\), so getting a number \(> 6\) is an impossible event.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

Impossible event has probability \(0\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q17Assertion-Reason
Assertion (A)
Probability of picking a number divisible by \(5\) from \(1\) to \(20\) is \(\frac{1}{5}\).
Reason (R)
Numbers divisible by \(5\) between \(1\) and \(20\) are \(5, 10, 15, 20, 25\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(\{5, 10, 15, 20\} = 4\) numbers, \(P = 4/20 = 1/5\)). Reason (R) is false because \(25\) is greater than \(20\).
Correct Answer: (C)

Assertion true; Reason false.
Q18Assertion-Reason
Assertion (A)
If \(P(E) = 0.05\), then \(P(\text{not } E) = 0.95\).
Reason (R)
\(P(\bar{E}) = 1 - P(E) = 1 - 0.05 = 0.95\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

\(P(\text{not } E) = 1 - 0.05 = 0.95\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q19Assertion-Reason
Assertion (A)
The probability of drawing a black king from a deck of \(52\) cards is \(\frac{1}{26}\).
Reason (R)
There are \(2\) black kings (Spades and Clubs) in a deck of \(52\) cards, so \(P = \frac{2}{52} = \frac{1}{26}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true calculations.
Correct Answer: (B)

Both true.
Q20Assertion-Reason
Assertion (A)
If the probability of winning a game is \(0.4\), the probability of losing it is \(0.6\).
Reason (R)
Winning and losing are complementary events, so \(P(E) + P(\bar{E}) = 1 \implies P(\bar{E}) = 1 - 0.4 = 0.6\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (A)

\(P(\bar{E}) = 1 - P(E) = 1 - 0.4 = 0.6\). Reason explains Assertion.
Correct Answer: (A)

Reason explains Assertion.
Q21Assertion-Reason
Assertion (A)
The probability of getting a sum of \(2\) when two dice are thrown is \(\frac{2}{36}\).
Reason (R)
The only favorable outcome for sum \(2\) is \((1, 1)\), so \(P = \frac{1}{36}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false (it is \(1/36\)). Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q22Assertion-Reason
Assertion (A)
For any event \(E\), \(0 \le P(E) \le 1\).
Reason (R)
The sum of probabilities of all elementary events of an experiment is \(1\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are fundamental axioms of probability theory.
Correct Answer: (B)

Both true.
Q23Assertion-Reason
Assertion (A)
When a coin is tossed once, probability of getting a head is \(\frac{1}{2}\).
Reason (R)
Sample space for tossing a coin is \(S = \{\text{Head}, \text{Tail}\}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true.
Correct Answer: (B)

Both true.
Q24Assertion-Reason
Assertion (A)
If a letter is chosen from English alphabet, probability that it is a vowel is \(\frac{5}{26}\).
Reason (R)
There are \(21\) vowels in English alphabet.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (vowels \(\{A, E, I, O, U\} = 5\)). Reason (R) is false because there are \(5\) vowels, not \(21\) (\(21\) is consonants).
Correct Answer: (C)

Assertion true; Reason false.
Q25Assertion-Reason
Assertion (A)
If \(P(E) = 0.65\), then \(P(\text{not } E) = 0.35\).
Reason (R)
\(P(E) + P(\text{not } E) = 100\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(1 - 0.65 = 0.35\)). Reason (R) is false because sum of probabilities is \(1\), not \(100\) (it is \(100\%\), but in decimal form it is \(1\)).
Correct Answer: (C)

Assertion true; Reason false.
Q26Assertion-Reason
Assertion (A)
The probability of a sure (certain) event is \(1\).
Reason (R)
A sure event contains all outcomes of the sample space \(S\), so \(n(E) = n(S)\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true definitions.
Correct Answer: (B)

Both true.
Q27Assertion-Reason
Assertion (A)
If a card is drawn from a deck of \(52\) cards, probability of it being a face card is \(\frac{3}{13}\).
Reason (R)
There are \(12\) face cards (\(4\) Kings, \(4\) Queens, \(4\) Jacks) in a deck, so \(P = \frac{12}{52} = \frac{3}{13}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true.
Correct Answer: (B)

Both true.
Q28Assertion-Reason
Assertion (A)
Probability of drawing an Ace from a deck of \(52\) cards is \(\frac{1}{13}\).
Reason (R)
There are \(4\) Aces in a deck of \(52\) cards, so \(P = \frac{4}{52} = \frac{1}{13}\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (B)

Both A and R are true calculations.
Correct Answer: (B)

Both true.
Q29Assertion-Reason
Assertion (A)
The probability of an event can be \(-0.5\).
Reason (R)
Probability \(P(E)\) can never be negative and always lies in interval \(0 \le P(E) \le 1\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (D)

Assertion (A) is false. Reason (R) is true.
Correct Answer: (D)

Assertion false; Reason true.
Q30Assertion-Reason
Assertion (A)
Probability of getting a multiple of \(3\) on rolling a die is \(\frac{1}{3}\).
Reason (R)
Multiples of \(3\) on a die are \(3, 6, 9\).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
Correct Option: (C)

Assertion (A) is true (\(\{3, 6\}\), \(P = 2/6 = 1/3\)). Reason (R) is false because \(9\) does not exist on a standard die.
Correct Answer: (C)

Assertion true; Reason false.

Live Practice – Probability AR

Q 1 of 10
Answered: 0