A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
A) 3/40,000
B) 1/3,600
C) 9/2,000
D) 1/60
E) 1/16
Probability of selecting siblings
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One option is to apply probability rules.LulaBrazilia wrote:A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
A) 3/40,000
B) 1/3,600
C) 9/2,000
D) 1/60
E) 1/16
So, for two siblings to be selected, 2 things must happen: we must select a junior who has a senior sibling AND the senior selected must be the sibling of the selected junior.
We get P(junior with sibling AND selected senior is sibling to selected junior)= P(junior with sibling) x P(selected senior is sibling to selected junior)
P(junior with sibling): there are 1000 juniors and 60 of them have senior siblings. So, P(junior with sibling)=60/1000
P(selected senior is sibling to selected junior): Once the junior has been selected, there is only 1 senior (out of 800 seniors) who is the sibling to the selected junior. So, P(selected senior is sibling to selected junior)= 1/800
So, the probability is (60/1000)x(1/800) = 3/40,000
The answer is A
Cheers,
Brent
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There are 60/1,000 chances to pick a sibling from the junior class, then only 1/800 chances to pick the matching sibling from the senior class. The probability that both happen is (60/1000)(1/800) = 3/40,000. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).
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