Two cards are drawn at random from a well - shuffled pack of 52 cards. what is the probability that either both are red or both are queens?

n(S) =  $C252$ = 1326

 Let  A = event of getting both red cards

and B = event of getting both queens

then  $A\cap B$ = event of getting two red queens

n(A) =  $C226$ = 325,   n(B) =  $C24$ = 6

  $n(A\cap B)=C22=1$

  $\therefore PA=\frac{325}{1326}, PB = \frac{6}{1326}$

  $PA\cap B=\frac{1}{1326}$

$\therefore$P ( both red or both queens) =  $PA\cup B$

=  $PA+PB-PA\cap B=$ $\frac{325}{1326}+\frac{1}{221}-\frac{1}{1326}$= $\frac{55}{221}$