Hello!
I am puzzled by the answer of a probability question which I got from one of the GMAT Prep Now videos.
Question: If a teacher randomly selects 2 students from a group of 4 boys and 4 girls, what is the probability that the selection contains at least 1 boy?
I know that there are 2 methods to solve this question:
1) P(at least 1 boy) = 1 - P(0 boys)
= 1- P(all girls)
= 1 - P(girl 1 AND girl 2)
= 1 - (4/8*3/7) = 1 - 3/14
= 11/14 [correct answer]
However, when I try to solve it using the other method (as below), I can't seem to get the same answer.
2) P(at least 1 boy) = P(1 boy or 2 boys)
= P(1 boy) + P(2 boys)
= 4/8 + (4/8*3/7)
= 1/2 + 3/14
= 10/14
I would appreciate someone pointing out to me where I went wrong. Was it a calculation mistake or a conceptual mistake?
Thank you very much!
I am puzzled by the answer of a probability question which I got from one of the GMAT Prep Now videos.
Question: If a teacher randomly selects 2 students from a group of 4 boys and 4 girls, what is the probability that the selection contains at least 1 boy?
I know that there are 2 methods to solve this question:
1) P(at least 1 boy) = 1 - P(0 boys)
= 1- P(all girls)
= 1 - P(girl 1 AND girl 2)
= 1 - (4/8*3/7) = 1 - 3/14
= 11/14 [correct answer]
However, when I try to solve it using the other method (as below), I can't seem to get the same answer.
2) P(at least 1 boy) = P(1 boy or 2 boys)
= P(1 boy) + P(2 boys)
= 4/8 + (4/8*3/7)
= 1/2 + 3/14
= 10/14
I would appreciate someone pointing out to me where I went wrong. Was it a calculation mistake or a conceptual mistake?
Thank you very much!
