Question

2. You have a deck of 52 cards and you deal three cards (one-by-one). (a) Find...

2. You have a deck of 52 cards and you deal three cards (one-by-one). (a) Find the conditional probability that the third card is a queen given that the first two cards are kings. (b) Find the conditional probability that the third card is a queen given that the first two cards are spades. (c) Find the conditional probability that the first card is a spade given that the second card is an ace and the third card is a king.

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Answer #1

a)conditional probability that the third card is a queen given that the first two cards are kings =P(select 1 queen from 4 out of remaining 50 cards) =4/50 =2/25

b)

conditional probability that the third card is a queen given that the first two cards are spades

=P(one of spade is queen and third card is queen)+P(none of spade is queen and third card is queen)

=(2/13)*(3/50)+(11/13)*(4/50)=1/13

c)

conditional probability that the first card is a spade given that the second card is an ace and the third card is a king

=13/52 =1/4

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