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

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) =}(2)/(14)=(1)/(7)`

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

In percentage, the probability will be

`\begin{gathered} (1)/((1)/(7))=(100)/(x) \\ \text{x =}(1)/(7)*100 \\ \text{x = 14.29\%} \end{gathered}`

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