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 Post subject: GMAT Probability
PostPosted: Mon May 13, 2013 9:53 am 
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Joined: Tue Apr 13, 2010 8:48 am
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Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be odd?
A. 3/14
B. 2/7
C. 1/3
D. 1/2
E. 12/21

(B) For the first die there are 6 possible numbers, for the second die there are 7 possible numbers. When both are rolled together there are (6)(7) = 42 possible combinations. On the first die there are 3 odd numbers and on the second die there are 4 odd numbers. There are (3)(4) = 12 possible combinations where both numbers are odd. The probability that both numbers will be odd is 12/42 = 2/7.
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How would I solve this if the question was:
If Jack rolls both dice what is the probability that AT LEAST ONE of the numbers will be odd?


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 Post subject: Re: GMAT Probability
PostPosted: Mon May 13, 2013 9:54 am 
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Joined: Fri Apr 09, 2010 2:11 pm
Posts: 459
In this case the number of all the possible combinations is the same: 6 × 7 = 42

Let us count the number of combinations that have at least one odd number:

3 × 3 = 9, when the number on six-sided dice is odd and the other one is even
3 × 4 = 12, when the number on seven-sided dice is odd and the other one is even
3 × 4 = 12, when both numbers are odd

In total it gives us 9 + 12 + 12 = 33 distinct combinations.
The probability is 33/42 = 11/14.


Another way, the faster one, is to count the probability that both numbers are even:
(3 × 3) / 42 = 9/42 = 3/14

And then use the fact that only one must happen:
- both numbers are even
- at least one number is odd

So the probability that AT LEAST ONE of the numbers will be odd = 1 - 3/14 = 11/14.


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