Question

Find the probability distribution of the number of successes in two tosses of a die, where a succeess is defined as

six appears on the die.

Answer 1

Let X be the random variable which denotes the number of six appears on atleast one die. So, X may have values 0 or 1.

P(X=0) =P (six does not appear on any of the die)

$=\frac{5}{6}\times \frac{5}{6}=\frac{25}{36}$

P(X=1) =P (six appears on atleast one of the die) $=\frac{11}{36}$

Thus , the required probability distribution is as follows

$\begin{array}{ccc}X& 0& 1\\ P\left(X\right)& \frac{25}{36}& \frac{11}{36}\end{array}$