Two cards are drawn' successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

Step-by-step solution

Let X denote the number of king. Since the card is drawn twice, 0,1 and 2 are possible values of X . Probability of getting a king in a single draw of a card is p= 4 52 = 1 13 , q= 12 13 aligned & P[X=0]=P[ no king ]=q q=q^2= 144 169 & P [ X =1]= P [ one king ]= pq + qp =2 pq = 24 169 & P [ X =2]= P [ two kings ]= pp = p ^2= 1 169 & Mean = x_ i p _ i & =0 144 169 +1 24 169 +2 1 169 & = 26 169 = 2 13 aligned Alternate method: Let getting a king be the success. p= 1 13 , q= 12 13 Since two cards are drawn with replac