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Cards probabilities

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Cards probabilities

by jfranco23 » Fri Mar 06, 2009 4:53 pm
6 cards numbered from 1 to 6 are placed in an empty bowl. Drawn one card and thenput it back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the 2 cards drawn is numbered 5?

A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 2/3
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by Feep » Fri Mar 06, 2009 5:24 pm
The answer is D.

If the total is eight, any number except for 1 may be first drawn from the bowl: 2, 3, 4, 5, 6. The second card then must be, respectively, 6, 5, 4, 3, 2 to complete the stated sum.

So, we have
2, 6
3, 5
4, 4
5, 3
6, 2

Of these, two feature the number 5. So, 2/5.
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