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Sum of 8 - GMAT Prep Exam pack 1

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by prata » Mon May 30, 2016 2:28 pm
Six cards numbered from 1 to 6 are placed in an empty board. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at ramdom 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?

1. 1/6
2. 1/5
3. 1/3
4. 2/5
5. 2/3
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by GMATGuruNY » Mon May 30, 2016 2:32 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?

A) 1/6
B) 1/5
C) 1/3
D) 2/5
E) 2/3
Ways to get a sum of 8:
2, 6
3, 5
4, 4
5, 3
6, 2

As the options in red indicate, 2 of the 5 ways include a card numbered 5.
Thus:
P(a card numbered 5 is drawn) = 2/5.

The correct answer is D.
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by Brent@GMATPrepNow » Mon May 30, 2016 2:34 pm
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]

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Brent
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by OptimusPrep » Mon May 30, 2016 7:42 pm
prata wrote:Six cards numbered from 1 to 6 are placed in an empty board. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at ramdom 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?

1. 1/6
2. 1/5
3. 1/3
4. 2/5
5. 2/3
Total ways of drawing 2 cards with replacement = 6*6 = 36
We need the sum to be 8. It is possible in the following ways:

(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Hence a total of 5 ways.
Out of these, only in two ways do we get a 5.

Hence the required probability = 2/5

Correct Option: D
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