There is a group of six people; among them are Mr X and Mr Y. Three persons are chosen at random without repetitions. Find the probability of choosing Mr X, but not Mr Y.

Question

anonymous · Answer

I'd start by figuring out the probability of choosing Mr. X -- he's 1 out of 6, and you pick 3 people, so what's the probability of picking Mr. X?

kropot72 · Answer

When the first person is chosen there is a 1 out of 6 chance of choosing Mr X or Mr Y.
When the second person is chosen there is a 1 out of 5 chance of choosing Mr X or Mr Y.
When the third person is chosen there is a 1 out of 4 chance of choosing Mr X or Mr Y.
Therefore the chance of choosing both Mr X and Mr Y is the product of the separate probabilities:
$$P(X+Y)=\frac{1}{6}\times \frac{1}{5}\times \frac{1}{4}=\frac{1}{120}$$

anonymous · Answer

@kropot72: This question asked for "Fnd the probability of choosing Mr X, *but not* Mr Y. "

kropot72 · Answer

You are quite right FoolForMath. So i shall try again:
When choosing the first person there is a 1 out of 6 chance of choosing Mr X.
When choosing the second person there is a 4 out of 5 chance of not choosing Mr Y.
When choosing the third person there is a 3 out of 4 chance of not choosing Mr Y.
Therefore the probability of choosing Mr X and not choosing Mr Y is the product of the separate probabilities of the sub-events:
$$P(XnotY)=\frac{1}{6}\times \frac{4}{5}\times \frac{3}{4}=\frac{12}{120}$$

anonymous · Answer

I think it may be a bit simpler, you can do it in just two steps. What is the probability of choosing Mr. X? He's 1 of 6, and you draw three times. That probability indicates the times when Mr. X is one of the three "in" slots, leaving two "in" slots and three "out" slots.

In that situation, what is the probability that Mr. Y will be in one of the "out" slots?

Multiply those probabilities together (the odds of X being in, and then, given that condition, the odds of Y being out) and you've got your answer.

@kropot72, I think your formula was missing the fact that on the second draw, if Mr. X wasn't picked the first time, he was still available to be picked.