A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

Let $F(x)$ be the cumulative distribution function (c.d.f.) of a continuous random variable $X$. If $F(b) = 0.7$ and $P(X > a) = 0.4$, then the value of $P(a < X < b)$ is ...

If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both A and B is $0.3$, in both B and C is $0.2$, in both A and C is $0.2$, and in all three is $0.1$, then the probability that the student succeeds in exactly one of these tests is......

The angle made by vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with x-axis and that with y-axis are respectively.