probability

Question

Five people are on a team. Two of them are selected at random to attend a competition.

How many different groups of two can be selected?

and if Mary is one of the five people in the team, what is the probability that she is selected to attend the competition?

my thought was she has a 1/5 chance of being chosen for the first person in the competition and a 1/4 chance of being chosen for the 2nd position

please explain how you got the answer, thanks

Answer 1

There are 10 possible selections i.e. the number of combinations of 5 things taken 2 at a time.

 

The easiest way to see the answer to the second part is to write the 10 possibilities down (use the numbers 1 to 5 and write the 10 possible pairs). You will see that each item of the 5 occurs in each of 4 pairs, i.e. the probability of a particular item being selected is 4/10.