Question

A) Suppose that four cards are drawn with replacement. Find the probability of getting at least one face card. B) Suppose that four cards are drawn without replacement. Find the probability of getting at least one king.

Answer 1

Total number of cards in the deck = 52

Total number of face cards in the deck = 12 ( 3 from each suits)

P( face card) = 12/52 = 0.2308

A) Let X be the number of face cards out of 4 drawn cards

X~ binomial ( 4, 12/52)

P( At least one face card) = P( X >=1 )

= 1- P( X=0)

= 1- ( 1- (12/52))^ 4

= 1- ( 40/52)^4\

= 1- 0.3501

= 0.6499

B)   Number of Kings in the suit = 4

4 cards are drawn without replacement

P( at least one king) = 1- P( No king)

= 1- [ (48/52) * (47/51) * (46/50) * (45/49) ]

= 1- 0.7187

= 0.2813