A and B are participating in the same contest, the probability of their winning are 5/8 and 1/4 respectively. What is the probability that neither of them will win the contest? Option 1: 7/36 Option 2: 31/36 Option 3: 5/36 Option 4: 1/3

Answer: 1/3. Solution: The probability of A winning is 5/8 and the probability of B winning is 1/4. The probability that A does not win: P(A doesn't win) = 1 - 5/8 = 3/8 The probability that B does not win: P(B doesn't win) = 1 - 1/4 = 3/4 For neither A nor B to win, both events must occur together. The probabilities are multiplied: P(Neither wins) = P(A doesn't win) x P(B doesn't win) = 3/8 x 3/4 = 9/32 The calculated answer is 9/32, which equals approximately 0.281 or 28.1%. None of the given options exactly match this answer. The mathematically correct answer is 9/32, but based on the answer key provided, Option 4 (1/3) is marked as correct, though there appears to be a discrepancy. Attaching official NTA answer key for reference.

Quantitative Reasoning

Probability

Easy

A and B are participating in the same contest, the probability of their winning are $\frac{5}{8}$ and $\frac{1}{4}$ respectively. What is the probability that neither of them will win the contest?

$\frac{7}{36}$

$\frac{31}{36}$

$\frac{5}{36}$

$\frac{1}{3}$

✅ Correct Option: 4

The probability of A winning is $\frac{5}{8}$ and the probability of B winning is $\frac{1}{4}$ .

The probability that A does not win:

$P(\text{A doesn't win}) = 1 - \frac{5}{8}$

$= \frac{3}{8}$

The probability that B does not win:

$P(\text{B doesn't win}) = 1 - \frac{1}{4}$

$= \frac{3}{4}$

For neither A nor B to win, both events must occur together. The probabilities are multiplied:

$P(\text{Neither wins}) = P(\text{A doesn't win}) \times P(\text{B doesn't win})$

$= \frac{3}{8} \times \frac{3}{4}$

$= \frac{9}{32}$

The calculated answer is $\frac{9}{32}$ , which equals approximately $0.281$ or $28.1\%$ .

None of the given options exactly match this answer. The mathematically correct answer is $\frac{9}{32}$ , but based on the answer key provided, Option 4 ( $\frac{1}{3}$ ) is marked as correct, though there appears to be a discrepancy.

Attaching official NTA answer key for reference.

Solution figure for CUET General Test 2025 29 May Shift 2 question 29 (Quantitative Reasoning)

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Choose the correct answer from the options given below:

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A and B are participating in the same contest, the probability of their winning are 58\frac{5}{8}85​ and 14\frac{1}{4}41​ respectively. What is the probability that neither of them will win the contest?

Solution

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CUET General Test Past Year Questions (Topic-Wise)

A and B are participating in the same contest, the probability of their winning are $\frac{5}{8}$ and $\frac{1}{4}$ respectively. What is the probability that neither of them will win the contest?