Two cards are drawn in succession from a standard 52card dec

Two cards are drawn in succession from a standard 52-card deck. Find the probability that the first card is a club and the second card is a heart, given the following constraints:

(a) the cards are drawn without replacement.

(b) the cards are drawn with replacement.

Solution

1-without replace ment

prob.of drawing a club=13/52=1/4

total cars left after one draw=51

prob.of drawing a heart=13/51

prob.of drawing two cards=(1/4)*(13/51)=13/204=0.0637

2-with replacement

total prob=(13/52)*(13/52)=1/16=0.0625