# NCERT Class 12-Mathematics: Chapter –13 Probability Part 2

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## 13.2 Solved Examples

### Short Answer (S.A)

**Question 1:**

A and B are two candidates seeking admission in a college. The probability that A is selected is and the probability that exactly one of them is selected is . Find the probability that B is selected.

**Answer:**

Let be the probability that B gets selected.

Thus the probability that B gets selected is .

**Question 2:**

The probability of simultaneous occurrence of at least one of two events A and B is . If the probability that exactly one of A, B occurs is , then prove that

**Answer:**

Since we get

**Question 3:**

of the bulbs produced in a factory are of red colour and are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.

**Answer:**

Let A and B be the events that the bulb is red and defective, respectively.

Thus the probability of the picked up bulb of its being defective, if it is red, is .

**Question 4:**

Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting on the second die’. Are the events A and B independent?

**Answer:**

Events A and B will be independent if

Hence, A and B are independent.

**Question 5:**

A committee of students is selected at random from a group consisting boys and girls. Given that there is at least one girl on the committee, calculate the probability that there are exactly girls on the committee.

**Answer:**

Let A denote the event that at least one girl will be chosen, and B the event that exactly 2 girls will be chosen. We require .

Since A denotes the event that at least one girl will be chosen, A denotes that no girl is chosen, i.e., boys are chosen. Then