An experiment consists of first tossing a 3 sided die which has letters A, B, an

Question

An experiment consists of first tossing a 3 sided die which has letters A, B, and C on each side and then choosing 2 cards sequentially from a deck without replacement. If you roll either an A or a B, then all the cards from 2-8 are removed from the deck so that there are only 24 cards consisting of 9, 10, J, Q, K, A (called a stripped deck). Then, from this stripped deck, the two cards are chosen. If you roll a C, then we draw the 2 cards from a standard 52 card deck.

a) What is the probability that both cards that are drawn are face cards?

b) What is the probability that both cards are face cards given that an A is rolled?

c) What is the probability of getting a pair?

d) What is the probability both cards have the same suit?

Explanation / Answer

a) P(both cards are face cards) = P(A or B and 2 face cards) + P(C and 2 face cards)

= 2/3 x 12/24 x 11/23 + 1/3 x 12/52 x 11/51

= 0.1760

b) P(both cards are face cards | A is rolled)

= 12/24 x 11/23

= 0.2391

c) P(getting a pair) = P(A or B and getting a pair) + P(C and getting a pair)

= 2/3 x 1x3/23 + 1/3 x 1 x 3/51

= 0.1066

d) P(both cards have same suit) = P(A or B and same suit) + P(C and same suit)

= 2/3 x1 x 5/23 + 1/3x 1 x 12/51

= 0.2234

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