If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is :

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) $F(\infty) = 1$

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Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is

If the difference between mean and variance of a Binomial distribution is 1 and the difference of their squares is 5, then the probability of success is

It is given that student marked the answer correctly, the probability that he guesses is

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II is :

A bag contains 4 balls. Let E be an event in which two balls are drawn at random and found to be white, then

Match List-I with List-II

Choose the correct answer from the options given below: