Probability (Class 12)

Three students S1, S2, and S3 are given a problem to solve. Consider the following events: U: At least one of S1, S2, and S3 can solve the problem, V: S1 can solve the problem, given that neither S2 nor S3 can solve the problem, W: S2 can solve the problem and S3 cannot solve the problem, T: S3 can solve the problem. For any event E, let P(E) denote the probability of E. If P(U) = 12, P(V) = 110, and P(W) = 112, then P(T) is equal to

1. 1336
2. 13
3. 1960
4. 14

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 12. Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is 16. Then the probability that the student knows the answer of a randomly chosen question is

1. 112
2. 17
3. 57
4. 512