Question

Suppose that 5 cards are selected (without replacement) at random from a regular deck of 52 playing cards:

a. If it is known that at least 2 hearts have been selected, what is the probability that at least 3 hearts have been selected?

b. If it is known that the queen of hearts has been selected, what is the probability that at least 3 hearts have been selected?

Answer #1

a) Given that 2 hearts have been selected probability that at least 3 hearts are selected is computed here as:

= P( >= 3 hearts have been selected ) / P( >= 2 hearts have been selected)

= Number of ways to select 5 cards such that >= 3 hearts are selected / Total number of ways to select 5 cards such that >= 2 hearts have been selected

**Therefore 0.2527 is the required probability
here.**

b) Given that queen of hearts has been selected, probability that at least 3 hearts have been selected is computed here as:

= Number of ways to select >= 3 hearts including the queen of hearts / Total number of ways to select 5 cards such that queen of hearts is selected

**Therefore 0.6051 is the required probability
here.**

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