Question

Shelley's basketball team won 3/4 of their games last season. In 1/6 of the games they won, they outscored their opponents by more than 10 points. What fraction of their games did Shelley’s team win by more than 10 points?

Answer 1

`(1)/(8)`

Explanation:

This problem can be resolved with a simple multiplication, but the important thing is to analyse and know why.

First of all, this problem can be seen as a probability problem with two events: Games won (Event A) and Games won with more than 10 points (Event B).

Each event have already its probability. For Event A we have
`(3)/(4)`. For Event B we have
`(1)/(6)`.

So, the fact that it's being asked for the expression when they won and with more than 10 points, means an interception, a mixture of both events. In order to that ''mixture'', mathematically we multiply, because we need to calculate games won and with more than 10 points.

`(3)/(4) . (1)/(6) = (3)/(24)  = (1)/(8)`

Answer 2

Let the total number of games be x.

Number of games Shelley's team won =
`(3)/(4) x`

Number of games they outscored

their opponents by more than 10 points =
`(1)/(6)` ×
`(3)/(4) x`

=
`(1)/(8) x`

Hence, 1/8 of the total games, Shelley's team won by 10 points.