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
OG Quant Review - # 80 (probability)
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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.
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.