Question

The names of eight boys and six girls from your class are put into a hat what is the probability that the first two names chosen will both be boys?

Answer 1

`4/13`

Explanation:

`color(blue)("Assumption: Selection without replacement."`

Let the probability of the first selection be `P_1`
Let the probability of the second selection be `P_2`

`color(brown)("At first selection from the hat there are:")`

8 boys + 6 girls `->` Total of 14

So `P_1= 8/14`

`color(brown)("Under the assumption that a boy was selected we now have:")`

7 boys + 6 girls`->` Total of 13

So `P_2= 7/13`

`color(blue)("Thus "P_1 " and " P_2 = 8/14xx7/13 = 4/13`