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 $5$?

a. $0.150$

b. $0.214$

c. $0.300$

d. $0.428$

e.$0.700$

Short answer

The correct option is b.$0.214$.

Step-by-step solution

Step 1. Given information

The table is:

Step 2. Explanation for correct option

Consider, the missing value be $x$.

It is known that sum of a probability distribution is equal to $1.$

Using this property, the missing value could be computed as:

$$\begin{gathered} 0.1+0.2+x+0.25+0.15=1 \\ x=1-0.70 \\ x=0.30 \end{gathered}$$

Thus, the complete table is:

Using the above table, the probability that random selected student score a $5$, if it is given that student earned a score of $3$or higher can be computed as:

$$\begin{gathered} P(Scoreis5|Scoreis3ormore)=\frac{P(Scoreis5andScoreis3ormore)}{P(Scoreis3ormore)} \\ =\frac{P(Scoreis5)}{P(Scoreis3ormore)} \\ =\frac{0.15}{0.30+0.25+0.15} \\ =0.214 \end{gathered}$$

The required probability is $0.214$

Hence, the correct option is (b).