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Probability: 5 numbered card

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by avanti@gmat » Sat Jul 19, 2014 8:14 am
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back. Then second card is drawn. If cards are drawn at random and is sum of numbers on cards is 8, what is the Probability that one of the two cards drawn is numbered 5?
1) 1/6
2) 1/5
3) 1/3
4) 2/5
5) 2/3
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by GMATinsight » Sat Jul 19, 2014 8:33 am
avanti@gmat wrote:Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back. Then second card is drawn. If cards are drawn at random and is sum of numbers on cards is 8, what is the Probability that one of the two cards drawn is numbered 5?
1) 1/6
2) 1/5
3) 1/3
4) 2/5
5) 2/3
Total Outcomes (sum of card=8) = {2,6} {3,5} {4,4} {5,3} {6,2} = 5
Favorable Total Outcomes = {3,5} {5,3} = 2

Probability = Favorable Outcomes/Total Outcomes

Probability = 2/5

Answer: Option D
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by avanti@gmat » Sat Jul 19, 2014 8:37 am
I completely missed it....thanks a lot
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by Brent@GMATPrepNow » Sat Jul 19, 2014 8:41 am
avanti@gmat wrote:Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back. Then second card is drawn. If cards are drawn at random and is sum of numbers on cards is 8, what is the Probability that one of the two cards drawn is numbered 5?
1) 1/6
2) 1/5
3) 1/3
4) 2/5
5) 2/3
There are 36 possible EQUALLY LIKELY outcomes in this scenario: (1,1), (1,2), (1,3)... etc.

Let's examine those outcomes where the sum is 8: (2,6), (3,5), (4,4), (5,3) and (6,2)
We're told that one of these five outcomes occurred, AND one of the numbers is a 5

Of those 5 outcomes, 2 meet the condition that one of the numbers is a 5, so the probability = [spoiler]2/5[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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