Quantitative Reasoning

Probability

Medium

Two candidates, X and Y appeared in an interview for two vacancies for the same post. The probabilities of their selection are 1/4 and 1/7, respectively. What is the probability that one of them will be selected?

1/28

27/28

5/14

9/28

✅ Correct Option: 4

Given:

Probability of X being selected = $\frac{1}{4}$

Probability of Y being selected = $\frac{1}{7}$

The question asks for the probability that exactly one of them will be selected.

The probability that X is not selected:

$P(\text{X not selected}) = 1 - \frac{1}{4}$

$P(\text{X not selected}) = \frac{3}{4}$

The probability that Y is not selected:

$P(\text{Y not selected}) = 1 - \frac{1}{7}$

$P(\text{Y not selected}) = \frac{6}{7}$

Exactly one candidate is selected when either:

X is selected and Y is not selected, OR
Y is selected and X is not selected

Probability that X is selected and Y is not selected:

$P(\text{X selected and Y not selected}) = \frac{1}{4} \times \frac{6}{7}$

$P(\text{X selected and Y not selected}) = \frac{6}{28}$

Probability that Y is selected and X is not selected:

$P(\text{Y selected and X not selected}) = \frac{1}{7} \times \frac{3}{4}$

$P(\text{Y selected and X not selected}) = \frac{3}{28}$

Probability that exactly one is selected:

$P(\text{exactly one selected}) = \frac{6}{28} + \frac{3}{28}$

$P(\text{exactly one selected}) = \frac{9}{28}$

Therefore, the probability that one of them will be selected is $\frac{9}{28}$ .

2025: 27 May Shift 2

Two dice are thrown simultaneously. What is the probability that 4 will come up on at least one die?

2026: 18 May Shift 1

Two unbiased coins are tossed:

Match the List-I and List-II

List-I	List-II
(A) Probability of getting one head	(I) 3/4
(B) Probability of getting two heads	(II) 1/2
(C) Probability of getting at most one head	(III) 1/4
(D) Probability of getting three heads	(IV) 0

Choose the correct answer from the options given below:

2026: 29 May Shift 1

Consider the experiment of rolling a die. Let A be the event 'getting a prime number', B be the event 'getting an odd number'. However C be the event containing only highest number of die. If P is the probability of the events.

(A) Here, $S = \{1,2,3,4,5,6\}, A = \{2,3,5\}, B = \{1,3,5\}, C = \{6\}$

(B) $A \cup B = \{1,2,3,5\}$ & $A \cap B = \{3,5\}$

(D) $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Arrange the above events in chronological order and choose the correct answer from the options given below:

2026: 22 May Shift 2

The probability that a card drawn from a pack of 52 cards will be a king or a diamond, is?

2025: 15 May Shift 1

A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct?

(A) The probability that both balls are red is 1/11.

(B) The probability that one ball is red, and one ball is blue is 10/33

(D) The probability that both balls are green is 5/11.

Choose the correct answer from the options given below:

2026: 6 June Shift 1

Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6?

Two candidates, X and Y appeared in an interview for two vacancies for the same post. The probabilities of their selection are 1/4 and 1/7, respectively. What is the probability that one of them will be selected?

Solution

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