Question

giving a test to a group of students, the grades and gender are summarized below
if one student was chosen at random, determine the following probabilities. write your answers as reduced fractions.
p(student was male) =
p(student was female) =
p(student was male and got an \a\) =
p(student was female and got a \b\) =
p(student got a \c\) =

Explanation:

Step1: Calculate \(P(\text{Student was male})\)

The formula for probability is \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The number of male students is \(40\), and the total number of students is \(74\). So \(P(\text{Student was male})=\frac{40}{74}=\frac{20}{37}\)

Step2: Calculate \(P(\text{Student was female})\)

The number of female students is \(34\), and the total number of students is \(74\). So \(P(\text{Student was female})=\frac{34}{74}=\frac{17}{37}\)

Step3: Calculate \(P(\text{Student was male and got an "A"})\)

The number of male students who got an "A" is \(13\), and the total number of students is \(74\). So \(P(\text{Student was male and got an "A"})=\frac{13}{74}\)

Step4: Calculate \(P(\text{Student was female and got a "B"})\)

The number of female students who got a "B" is \(11\), and the total number of students is \(74\). So \(P(\text{Student was female and got a "B"})=\frac{11}{74}\)

Step5: Calculate \(P(\text{Student got a "C"})\)

The number of students who got a "C" is \(33\), and the total number of students is \(74\). So \(P(\text{Student got a "C"})=\frac{33}{74}\)

Answer:

\(P(\text{Student was male})=\frac{20}{37}\)
\(P(\text{Student was female})=\frac{17}{37}\)
\(P(\text{Student was male and got an "A"})=\frac{13}{74}\)
\(P(\text{Student was female and got a "B"})=\frac{11}{74}\)
\(P(\text{Student got a "C"})=\frac{33}{74}\)