Question

Music class of 9th and 10th. Two students will be picked same time. There are 9 males in 9th and 8 males in 10th. There are12 females in 9th and 11 girls in the 10th. What is the probability both students are male?

Answer 1

`136/780~~17.4%`

Explanation:

There are 17 males and 23 females in the combined class, for a total of 40 students total. From these 40, 2 are to be picked. We can find the number of ways they can be picked by looking at the combinations general formula (we're using combinations because we don't care about the order in which they are picked):

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

`C_(40,2)=(40!)/((2!)(38!))=(40xx39)/2=780` ways 2 children can be picked.

We can see the number of ways only 2 males will be picked by limiting our choices to only the males: 17 in the class and we're picking 2:

`C_(17,2)=(17!)/((2!)(15!))=(17xx16)/2=136` ways.

And so the probability of picking 2 males is:

`136/780~~17.4%`