giving a test to a group of students, the grades and gender are summarized below\n| | a | b | c | total…

giving a test to a group of students, the grades and gender are summarized below\n| | a | b | c | total |\n|--|--|--|--|--|--|\n| male | 5 | 14 | 12 | 31 |\n| female | 20 | 13 | 10 | 43 |\n| total | 25 | 27 | 22 | 74 |\nif one student was chosen at random, determine the following probabilities. write your answers as reduced fractions.\np(student was male) =\np(student was female) =\np(student was male and got an \a\) =\np(student was female and got a \b\) =\np(student got a \c\) =

giving a test to a group of students, the grades and gender are summarized below\n| | a | b | c | total |\n|--|--|--|--|--|--|\n| male | 5 | 14 | 12 | 31 |\n| female | 20 | 13 | 10 | 43 |\n| total | 25 | 27 | 22 | 74 |\nif one student was chosen at random, determine the following probabilities. write your answers as reduced fractions.\np(student was male) =\np(student was female) =\np(student was male and got an \a\) =\np(student was female and got a \b\) =\np(student got a \c\) =

Answer

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:

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