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