Probability (Class 12)

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let E1 be the event that the ball chosen belonged to Box I and let E2 be the event that the ball chosen belonged to Box II. Let F1 be the event that the ball chosen is red and let F2 be the event that the ball chosen is green. Then which of the following statements is (are) TRUE ?

1. The events E1 and F1 are independent
2. The events E2 and F2 are dependent
3. The conditional probability P(F1 E1) is equal to the conditional probability P(F1 E2)
4. The conditional probability P(F1 E1) is greater than the conditional probability P(F2 E2)

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