Question

Below, the two-way table is given for a class ofstudents.Freshmen SophomoreJuniorsSeniors TotalMale4622Female 3463TotalIf a student is selected at random, find theprobability the student is a male given that it's asenior.r

Answer 1

The probability of male given senior can be given the formula:

`P(male\text{ \mid senior\rparen = }\frac{P(male\text{ and senior\rparen}}{P(senior)}`

Recall the probability of an event e can be calculated using the formula:

`P(an\text{ event e occurring\rparen= }\frac{Number\text{ of expected outcomes}}{Total\text{ number of possible outcomes}}`

From the table, we have:

Total number of students = 30

Total number of seniors = 5

Total number of males that are seniors = 2

Substituting the values into the formula:

`\begin{gathered} P(male\text{ \mid Senior\rparen = }((2)/(30))/((5)/(30)) \\ =\text{ 0.4} \\ Converting\text{ to \%} \\ P(male\text{ \mid Senior\rparen = 40\%} \end{gathered}`

Answer: 40%