Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

Step-by-step solution

Let X denote the number of queens. Possible values of X are 0,1,2 . aligned & P ( queen )= 4 52 = 1 13 & aligned P ( not a queen ) & = 48 52 = 12 13 P ( X =0) & = 12 13 12 13 & = 144 169 P ( X =1) & = ( 1 13 12 13 )+ ( 12 13 1 13 ) & = 12 169 + 12 169 = 24 169 P ( X =2) & = 1 13 1 13 & = 1 169 aligned aligned array |c|c|c|c| X =x & 0 & 1 & 2 P [ X =x] & 144 169 & 24 169 & 1 169 array The probability distribution of X is