Question

A class has 10 boys (including Doug) and 8 girls (including Cathy).

If 3 students are chosen at random to be studyhall monitors, what is the probability that Doug is selected but Cathy is not?

Answer #1

We are given that, the class has 10 boys and 8 girls.

Following are the combinations for 3 students selected to include Doug and not Cathy

3 boys = 10C3

2 boys, 1 girl = 10C2 * 7C1 (Since Cathy is not selected)

1 boy, 2 girls = 10C1 * 7C2 (Since Cathy is not selected)

0 boys, 3 girls = 7C3

Probability that 3 students selected include Dough but not Cathy =

=

**Probability that Doug is selected but Cathy is not is
0.833**

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