Question

The partially complete table that follows shows the distribution of scores on the AP®

Statistics exam for a class of students.

Select a student from this class at random. If the student earned a score of 3 or higher

on the AP® Statistics exam, what is the probability that the student scored a 5?

$$\begin{gathered} a.0.150 \\ b.0.214 \\ c.0.300 \\ d.0.428 \\ e.0.700 \end{gathered}$$

Short answer

The correct option is:

$b.0.214$is the probability that the student scored a$5$

Step-by-step solution

Given information

We have to find the is the probability that the student scored a$5$.

Explanation

Assuming that a single person cannot have more than one score, we may use the addition rule to solve for mutually exclusive events:

$P\left(\text{Score is at least}3\right)=P\left(\text{Score is}3\right)+P\left(\text{Score is}4\right)+P\left(\text{Score is}5\right)$

$=0.70$

$P(\text{Score is}5\mid \text{Score is at least}3)=\frac{P\left(\text{Score is}5\text{and Score is at least}3\right)}{P\left(\text{Score is at least}3\right)}$

$=\frac{15}{70}$

$\approx 0.214$