Suppose that 4 cards from a standard deck of 52 playing card

Suppose that 4 cards from a standard deck of 52 playing cards are successively drawn at random without replacement.

(A) find the probability that all 4 are queens.

(B) find the probability that all 4 are diamonds.

Answer:

a) The probability of drawing all 4 queens without replacement:

p(queen in the first draw) = 4/52

p(queen on the second draw) = 3/51

p(queen on the third draw) =2/50

p(queen on the fourth draw) =1/49

Thus p(4 queens) = (4*52)*(3/51)*(2/50)*(1/49) = 0.000003693

b) Similarly, p(all 4 diamonds) = p(diamond on first draw)*p(diamond on the second draw)*p(diamond on third draw)*p(diamond on fourth draw)

= (13/52)*(12/51)*(12/50)*(11/49)= 0.9093