Question

Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a student is selected at random, find theprobability the student is a male given that it's asophomore.

Answer 1

The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.

We want to calculate the probability the student is a male given that it's a sophomore. Since we already know the student is a sophomore, the possible outcomes are only male sophomores(6) and female sophomores(4) and the favourable outcomes are the male sophomores(6), therefore, this probability is:

`P(Male|Sophomore)=(6)/(6+4)=(6)/(10)=(60)/(100)=60\%`

The probability the student is a male given that it's a sophomore is 60%.