suppose we draw 2 cards out of deck of 52 let a the first ca

suppose we draw 2 cards out of deck of 52. let a= the first card is an ace and b=the second card is spade. are A and B independent?

If A and B are independent then P(A and B) = P(A) * P(B)

Here P(A) = 4/52 = 1/13

P(B) = P(spade in the first draw) * P( spade in the second draw) + P(not spade in the first draw ) * P(spade in the second draw)

= (13/52)*(12/51) + ( 39/52) * (13/52) =663/2652

P(A and B) = P(ace spade ) * P( spade ) + P(ace but not spade) * P( spade) = (1/52) * (12/51) + (3/52) * (13/51)

= 51/2652 =0.019231

P(A)*P(B) = (1/13)*(663/2652) = 0.019231

The events A, B are independent.