A fair die is tossed twice in succession. If $\mathrm{X}$ denotes the number of fours in two tosses, then…
A fair die is tossed twice in succession. If $\mathrm{X}$ denotes the number of fours in two tosses, then the probability distribution of $\mathrm{X}$ is given by
A fair die is tossed twice in succession.
$\therefore \quad$ Sample space (S)
$\begin{aligned}
= & (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), \\
& (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), \\
& (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), \\
& (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), \\
& (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), \\
& (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}
\end{aligned}$
$X:$ Number of fours in two tosses.
$\therefore \quad$ Possible values of $\mathrm{X}$ are: $0,1,2$.
$\therefore \quad$ Probability distribution of $\mathrm{X}$ is as follows:
$\begin{array}{|c|c|c|c|}
\hline X=x_{i} & 0 & 1 & 2 \\
\hline P_{i} & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\
\hline
\end{array}$