Mary and John are sister and brother. They are among the five students in their school trying out for the school team to play in an inter-school tournament. If the team is chosen randomly, what are the chances that both Mary and John are on the team?
Solution
When the first person is chosen for the team, there is a 2/5 chance that it is either Mary or John. When the second person is chosen, there is a 1/4 chance that it is the other one. By multiplying the probabilities we can see that the chance of both being chosen is 2/5 x 1/4, which equals 2/20, or 1/10.
There are 10 ways that two people can be chosen from a group of 5:
1, 2 2, 3 3, 4 4, 5
1, 3 2, 4 3, 5
1, 4 2, 5
1, 5
Only one of these ways is both Mary and John, so the chances that Mary and John are both chosen is 1 in 10.
Extension
What if seven students try out for the team? What is the chance of both Mary and John being chosen?
What if there are 159 students in the school try out for the badminton team? What is the chance of Mary and John being chosen?