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Cards probablility

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Junior | Next Rank: 30 Posts
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by apuso » Thu Jan 21, 2010 7:15 pm
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put 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 two cards drawn is numbered 5 ?
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by ace_gre » Thu Jan 21, 2010 8:00 pm
No. of ways of drawing 1st card = 6
No. of ways of drawing 2nd card = 6

Prob of 5 being first card ==> 1/6
Prob of 3 being second card = 1/6

Total probability = 1/36 * 2 because 5 can be second and 3 can be first...
Probability = 1/18

IMO 1/18
Is this correct?
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by apuso » Thu Jan 21, 2010 8:59 pm
Answer choices are:
A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 2/3

and OA is D
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by sreak1089 » Thu Jan 21, 2010 9:41 pm
apuso & ace_gre, this is a Conditional probability problem, hence it needs to be approached differently. Please take a note of the following statement:

"If the cards are drawn at random and if the sum of the numbers on the cards is 8".

We already know that the sum of the number on two cards is 8. Thus there are 5 possibilities (3,5), (5,3), (6,2), (2,6) and (4,4). Remember first card is put back after it is drawn.

Of the above 5 possibilities, only two are favorable [(3,5) and (5,3)]. Thus the probability is 2/5 (40%). Hence D.
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