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:

1) Mr X, but not Mr Y.
2) Both Mr X and Mr Y.
3) Neither Mr X nor Mr Y.
4) Either Mr X or Mr Y, but not both.
5) Either Mr X or Mr Y or both.

Question

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: 

1) Mr X, but not Mr Y. 
2) Both Mr X and Mr Y. 
3) Neither Mr X nor Mr Y. 
4) Either Mr X or Mr Y, but not both. 
5) Either Mr X or Mr Y or both.

anonymous · Answer

This is a statistical probability question without replacement.

You're best bet is to work through each number by imagining you are choosing one person at a time. Then choosing another from what is left. Reason with what the probability is each time. 

To start, 1) 
your first "choosing" can either be Mr X (1/6), Mr Y (1/6), or other (4/6).
Try making a tree diagram for each scenario and then multiply the probabilities leading up to the end result after 3 random people are chosen. add up the end probabilities of combinations where Mr.X got chosen but Mr. Y did not.