Bowl X has 4 cards in it, numbered 1 - 4. Bowl Y has 5 cards in it, numbered 5 - 9. What is the probability that the sum of a card pulled randomly from Bowl X and a card pulled randomly from Bowl Y will equal 8?

A. 1/20
B. 1/10
C. 3/20
D. 2/16
E. 3/16
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NOTE: In order to get a sum of 8, the card selected from Bowl X must be 1, 2 or 3.
Here's why: Cards 1, 2 and 3 all have corresponding cards in Bowl Y that add to get 8 (i.e., 1+7 = 8, 2+6 = 8 and 3+5 = 8)
However, card 4 (from Bowl X) does NOT have a corresponding card in Bowl Y that add to get 8.

So P(sum is 8) = P(card selected from Bowl X is 1, 2 or 3 AND card selected from Bowl Y is the one card that works with the first card to get a sum of 8)
= P(card selected from Bowl X is 1, 2 or 3) x P(card selected from Bowl Y is the one card that works with the first card to get a sum of 8)
= 3/4 x 1/5
= 3/20

Answer: C

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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