Question

One student from a music class is randomly selected on the first day of class. There is an 80% chance that the student arrived on time, and a 20% chance that the student arrived on time and is a female student.
What is the probability that the chosen student is a male student, given that the student arrived at class on time?
Write as a percent and round to the nearest tenth.

Answer 1

Denote A the event "The student arrivent on time"
F the event "The student arrivent on time and is a female"
M the event "The student arrivent on time and is a male"
We have the formula:
$P(A)=\times P(F)+\times P(M)$
In numbers we get:
$0.8=\times 0.2+\times P(M)$
Solving for P(M) we get:
$P(M)=0.8-0.5\times 0.2=0.7$

Answer 70%