Three cards are drawn successively with replacement from a well-shuffled deck of 52 cards. A random variable `X` denotes the number of hearts in the three cards drawn. determine the probability distribution of X.

Explanation

`x`(no. of hearts)
out of total `52` cards,`13` cards are heart.
`p(x=0)=39/52xx39/52xx39/52`
`=3/4xx3/4xx3/4=27/64`
`p(x=1)=(3c)_1(13/52xx39/52xx39/52)`
`=3xx1/4xx3/4xx3/4`
`=27/64`
`p(x=2)=(3c)_2(13/52xx13/52xx39/52)`
`=3xx1/4xx1/4xx3/4`
`=9/64`
`p(x=3)=13/52xx13/52xx13/52`
`=1/4xx1/4xx1/4=1/64`