Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

If A and B are independent events and $P(A) = \frac{1}{2}$ $P(B) = \frac{1}{3}$, then

Match List-I with List-II

Choose the correct answer from the options given below:

A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then

(A). P(Problem solved) = $\frac{3}{4}$

(B). P(Problem not solved) = $\frac{1}{4}$

(C). P(Problem solved by exactly one student) = $\frac{7}{24}$

(D). P(Problem solved by at least 2 students) = $\frac{17}{24}$

Choose the correct answer from the options given below:

Let $F(z)$ be the cumulative density function of the standard normal variate $z$, then which of the following are correct?

(A) $F(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-\frac{z^2}{2}} dz$, $-\infty < z < \infty$

(B) $F(-z) = 1 - F(z)$

(C) $F(0) = 0$

(D) $F(\infty) = 1$

Choose the correct answer from the options given below:

If A speaks truth in 75% cases and B speaks truth in 80% cases, then the probability that they contradict each other in a statement, is:

The probability of answering a question correctly, is :

Let x denotes the number of heads in a simultaneous toss of three coins, then $P(0 < x \leq 3)$