Question

Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0 reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?

Answer 1

The probability is:
`(55)/(60)` or
`(11)/(12)`

Explanation:

We know that probability of an event is given by:

`Probability=(Number of favourable outcome)/(Total number of possible outcome)`

here we are asked to find the probability that a student with GPA<3.0 does not enjoy the school.

we are given that the total number of students with GPA<3.0=60

out of these 60 students 5 enjoy the school so the remaining that do not enjoy school is 55.

hence, here number of favourable outcome=55

total number of possible outcome=60

hence,
`Probability=(55)/(60)=(11)/(12)`

Hence, the probability that a student with GPA<3.0 does not enjoy school is
`(55)/(60)` or
`(11)/(12)`.

Answer 2

Since what is ask is about the students whose GPA is below 3.0, then we will only focus on the sample population of 60 students. If 5 said they enjoyed school, then the rest of the 55 must not enjoy school. Thus, the probability would be 55/60 or 11/12 in its simplest form.