Two students are selected from a class of 5 girls and 12 boys. Find th

Question

Two students are selected from a class of 5 girls and 12 boys. Find the probability that a particular pair of girl and boy is selected.

(A) 1/136
(B) 1/63
(C) 1/51
(D) 10/21
(E) 13/61

Nidzo · Answer

Probability that one of the two particular boy and girl are selected: 2/17.
Probability that the other one is selected next: 1/16

(2/17)*(1/16)
= 1/136

Answer A

SergejK · Answer

But why not 1/5x1/12?

Alec0 · Answer

Bumping on this question. I also tried to solve via 1/5x1/12.

Bunuel

Bunuel · Answer

Say we want Alice and Bob to be selected.

P(Alice and Bob) = P(first Alice, second Bob) + P(first Bob, second Alice) = 1/17 * 1/16 + 1/17 * 1/16.

Or, we can do: 1C1 * 1C1 / 17C2 = 1/(8 * 17) = 1/136.

Hope this helps.

percyboi66 · Answer

Here's my solution:

we're selecting 2 students from a total of 5 + 12 = 17. Therefore total combinations = 17C2 = 17!/(2!)(15!) = 136

We only need to find the probability of one specific pair so there's only one correct outcome which means the probability is 1/136

Answer is A

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