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OG Quant Review - # 80 (probability)

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Junior | Next Rank: 30 Posts
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by sachin.ranjit » Mon Jun 23, 2008 12:34 pm
If X is to be chosen at random from the set {1,2,3,4} and y is to be chosen from the set {5,6,7}, what is the probability that xy will be even?

a. 1/6
b. 1/3
c. 1/2
d. 2/3
e. 5/6

I searched for this problem, but couldnt find it in the forum. Please provide the link if this has already been discussed.

Thanks
Sachin
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Junior | Next Rank: 30 Posts
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by leovonp » Mon Jun 23, 2008 2:21 pm
I tackled it like this:

For xy to be even you need either x, y or both x and y to be even.

Paraphrasing the question: "what is the probability that at least x or y are even.

You can now solve this the easiest way by calculating the probability that neither of them is even and then subtracting the result from 1.

Odd Numbers: You have 2/4 from the first set and 2/3 from the second. Multiply the two fractions with each other in order to get the probability of xy to be odd. Subtract the result from 1 to get the probability that xy is even.
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