Question

a test was given 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 simplified fractions.
a. p(student was male) is equal to
b. p(student was female) is equal to
c. p(student was male and got an \a\) is equal to
d. p(student was female and got a \b\) is equal to
e. p(student got a \c\) is equal to
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Explanation:

Step1: Calculate probability formula

The probability formula is \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of students \(n = 79\).

Step2: Solve for \(P(\text{Student was male})\)

The number of male students \(n_{\text{male}}=24\). So \(P(\text{Student was male})=\frac{24}{79}\).

Step3: Solve for \(P(\text{Student was female})\)

The number of female students \(n_{\text{female}} = 55\). So \(P(\text{Student was female})=\frac{55}{79}\).

Step4: Solve for \(P(\text{Student was male and got an "A"})\)

The number of male students who got an "A" \(n_{\text{male - A}}=5\). So \(P(\text{Student was male and got an "A"})=\frac{5}{79}\).

Step5: Solve for \(P(\text{Student was female and got a "B"})\)

The number of female students who got a "B" \(n_{\text{female - B}}=20\). So \(P(\text{Student was female and got a "B"})=\frac{20}{79}\).

Step6: Solve for \(P(\text{Student got a "C"})\)

The number of students who got a "C" \(n_{C}=26\). So \(P(\text{Student got a "C"})=\frac{26}{79}\).

Answer:

A. \(\frac{24}{79}\)
B. \(\frac{55}{79}\)
C. \(\frac{5}{79}\)
D. \(\frac{20}{79}\)
E. \(\frac{26}{79}\)