Question

In a group of students at a four-year college,60 percent of the students are 25 years old orolder and 25 percent of the students have a gradepoint average of 3.0 or better. The age of astudent is independent of their grade pointaverage. What is the probability that a studentrandomly selected from this group will be25 years old or older and will have a gradepoint average of 3.0 or better?

Answer 1

Let's call event A the event of being 25 years old or older, and event B the event of having a grade point average of 3.0 or better.

In order to calculate the probability of events A and B happening, we can use the formula below:

$P(A\cap B)=P(A)\cdot P(B|A)$

Since the events are independent, we have:

$P(B|A)=P(B)$

So, calculating the probability of both events at the same time:

$\begin{gathered} P(A\cap B)=P(A)\cdot P(B) \\ P(A\cap B)=0.6\cdot0.25 \\ P(A\cap B)=0.15 \end{gathered}$

Therefore the probability is 15%.