Bunuel wrote:

A card shop contains 5 birthday cards, 5 holiday cards, and 5 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type?

A. 6/91

B. 5/93

C. 4/95

D. 3/97

E. 2/99

Let's first rewrite our probability and then apply probability rules.

P(All 3 cards the same type) = P(1st card is ANY type

AND 2nd card matches type of 1st card

AND 3rd card matches type of 1st card)

= P(1st card is ANY type)

x P(2nd card matches type of 1st card)

x P(3rd card matches type of 1st card)

= 1

x 4/14

x 3/13

= 6/91

Answer: A

ASIDE

P(1st card is ANY type) =1 because the first selection can be any type

P(2nd card matches type of 1st card) = 4/14, because once the 1st card is selected, there are 14 cards remaining, and there are 4 cards left that are the same type as the first card

P(3rd card matches type of 1st card) = 3/13, because once cards 1 and 2 have been selected, there are 13 cards remaining, and only 3 of them are the same type as the first card

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com