Three boxes contain respectively $3$ white and $1$ black,$2$ white and $2$ black,$1$ white and $3$ black balls. From each of the boxes,one ball is drawn at random. The probability that $2$ white and $1$ black balls will be drawn is:

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.

$A$ pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in the first throw and composite numbers on both the dice in the second throw is

The probability that a non-leap year contains $53$ Sundays is

$A$ box contains $1$ red and $3$ identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd,the coin is tossed twice. Write the sample space for this experiment.