Consider the following relations for two events E and F :

1. P(E ∩ F) ≥ P(E) + P(F) - 1

2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F)

3. P(E ∪ F) ≤ P(E) + P(F)

Which of the above relations is/are correct?

If P(A|B) < P(A), then which one of the following is correct?

A problem is given to three students A, B and C, whose probabilities of solving the problem independently are $\rm \frac{1}{2}$, $\rm \frac{3}{4}$ and p respectively. If the probability that the problem can be solved is $\rm \frac{29}{32}$, then what is the value of p?

In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?