Question

giving a test to a group of students, the grades and gender are summarized below

	a	b	c	total
female	20	13	10	43
total	25	27	22	74

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: Recall probability formula

The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the total number of elements in the sample - space. Here, $n(S) = 74$.

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

The number of male students $n(\text{Male})=31$. So $P(\text{Student was male})=\frac{31}{74}$.

Step3: Calculate $P(\text{Student was female})$

The number of female students $n(\text{Female}) = 43$. So $P(\text{Student was female})=\frac{43}{74}$.

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

The number of male students who got an "A" is $5$. So $P(\text{Student was male and got an "A"})=\frac{5}{74}$.

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

The number of female students who got a "B" is $13$. So $P(\text{Student was female and got a "B"})=\frac{13}{74}$.

Step6: Calculate $P(\text{Student got a "C"})$

The number of students who got a "C" is $22$. So $P(\text{Student got a "C"})=\frac{22}{74}=\frac{11}{37}$.

Answer:

$P(\text{Student was male})=\frac{31}{74}$
$P(\text{Student was female})=\frac{43}{74}$
$P(\text{Student was male and got an "A"})=\frac{5}{74}$
$P(\text{Student was female and got a "B"})=\frac{13}{74}$
$P(\text{Student got a "C"})=\frac{11}{37}$