Correct Answer - B
Let us number the cards as 1,2,3,..,52. Also, let Ai(i=1,2,..,52)
denote the event that ith
card is common in the two draws of two cards each. Then,
Required probability =P(A1∪A2∪..∪A52)
=
52
∑
r=1
P(Ar)
=
52
∑
r=1
Probability that the cards marked r is common to two draws of two cards each.
=
52
∑
r=1
(Probability of a drawing the card marked r and any other card) ×
(Probability of B drawing the card make r and any other card)
=
52
∑
r=1
(
.51C1
.52C2
×
.50C1
.52C2
)=52×
51
51×26
×
50
51×26
=
50
663
