Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

Explanation

in a deck, 4 aces

p(ace)=`4/52 = 1/13`

p(ace`'`)`= 1 - 1/13 = 12/13`

x= no of aces

`x= {0,1,2}`

`p(x=0)= 12/13*12/13=144/169`

`p(x=1) = 12/13*1/13 + 1/13*12/13 = 24/169`

`p(x=2) = 1/13*1/13 = 1/169`

...