There are three identical boxes I, II and III, each containing two balls. In box I, both balls are red, In box II, both balls are blue and box III contains one blue ball and one red ball. A boy randomly chooses a box and takes out a ball at random from it. If the ball is red, then the probability that the other ball in the box is also red colour is:

A company manufactured a product through 4 units. A, B, C and D. The probability that a product is manufactured are $\frac{3}{10},\frac{1}{5},\frac{1}{10}$ and $\frac{2}{5}$ by units A, B, C and D respectively. The probability that it will be defective are $\frac{1}{4},\frac{1}{3}$ and $\frac{1}{12}$ if it is produced by A, B, C respectively and there is no defective from unit D. A product is chosen, it is found to be defective.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A lot of 50 watches is known to have 10 defective watches. If 8 watches are selected one by one with a replacement at random, then the probability that there will be at least one defective watch is:

If $P(A) = \frac{3}{5}$, $P(B) = \frac{1}{2}$ and $P(A \cap B) = \frac{1}{4}$, then $P(\overline{A} | \overline{B})$ is

Let X be the random variable with probability distribution given by the following table.

The value of $P(X \leq 1)$ is:

If A and B are two events such that $P(A) \neq 0$, $P(B) \neq 1$ and $P(\bar{A}/\bar{B}) = \frac{1-k}{P(\bar{B})}$, then the value of $k$ is

Ten cards are numbered from 1 to 10. A and B are playing a game by drawing a card, alternately, with replacement, till one gets a prime number then the probability of B's winning if A started the game is