Question

Observe that a deck of poker cards consists of 4 aces, 12 face cards (Jacks, Queens, and Kings), and 36 numbered cards (from 2s to 10s). If 10 cards are drawn from a deck of cards (with replacement and reshuffling after each draw), what is the probability that:

(a) The 10 cards contain exactly 1 ace, 3 face cards, and 6 numbered cards?

(b) The 10 cards contain at least three cards of each type (i.e. aces, face cards, numbered cards)?

Answer 1

here as P(ace)=4/52 =1/13 ; P(face cards) =12/52 =3/13 and P(numbered card)=36/52=9/13

a)P( 10 cards contain exactly 1 ace, 3 face cards, and 6 numbered cards )

= =0.087431

b)P( 10 cards contain at least three cards of each type )=P( 10 cards contain exactly 3 ace, 3 face cards, and 4 numbered cards )+P( 10 cards contain exactly 3 ace, 4 face cards, and 3 numbered cards )+P( 10 cards contain exactly 4 ace, 3 face cards, and 3 numbered cards )

=++ =0.007796