Chapter 5, Problem T5.7SPT

To determine

To find: The probability that random selected student score a 5, if it is given that student earned a score of 3 or higher.

Answer to Problem T5.7SPT

The probability is 0.214..

Explanation of Solution

Given:

The table is:

Score	1	2	3	4	5
Probability	0.1	0.2	????	0.25	0.15

Calculation:

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:

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

Thus, the complete table is:

Score	1	2	3	4	5
Probability	0.1	0.2	0.30	0.25	0.15

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:

  $\begin{array}{c}P\left(\text{Score is 5|Score is 3 or more}\right)=\frac{P\left(\text{Score is 5 and Score is 3 or more}\right)}{P\left(\text{Score is 3 or more}\right)}\\ =\frac{P\left(\text{Score is 5}\right)}{P\left(\text{Score is 3 or more}\right)}\\ =\frac{0.15}{0.30+0.25+0.15}\\ =0.214\end{array}$

The required probability is 0.214.

Hence, the correct option is (b).