Question

A fair die is tossed twice. If the number appearing on the top is less than 3, it is a success. Find the probability distribution of number of successes.

Answer 1

Let X denote the event of getting a number less than 3 (1 or 2) on throwing the die. Then, X can take the values 0, 1 and 2.
Now,
$$\begin{gathered} P\left(X=0\right)=\frac{16}{36}=\frac{4}{9} \\ P\left(X=1\right)=\frac{16}{36}=\frac{4}{9} \\ P\left(X=2\right)=\frac{4}{36}=\frac{1}{9} \end{gathered}$$

Thus, the probability distribution of X is given by

X	P(X)
0	$\frac{4}{9}$
1	$\frac{4}{9}$
2	$\frac{1}{9}$