Question

FreshmenSophomoreJuniors464Below, the two-way table is given for aclass of students.Seniors TotalMale2 2Female 36 3TotalIf a student is selected at random, find theprobability the student is a junior given that it'smale. Round to the nearest whole percent.[?]%

Answer 1

Solution

Step 1

Write out the expression for the probability of an event occurring

$Pr(\text{ event occurring)}=\frac{Number\text{ of required events}}{\text{Total number of events}}$

For this question,

The number of required events = The number of students that are male and Junior= 2

The total number of events = The total number of male students= 4+6+2+2 = 14

Step 2

Find the required probability after substitution

$Pr(\text{student }is\text{ a junior given its male) =}\frac{2}{14}=\frac{1}{7}$

Hence the probability the student is a junior given its a male = 1/7

In percentage, the probability will be

$\begin{gathered} \frac{1}{\frac{1}{7}}=\frac{100}{x} \\ \text{x =}\frac{1}{7}\times100 \\ \text{x = 14.29\%} \end{gathered}$

Where x is the required percentage, to the nearest whole percent, the final answer is 14%