Question

after giving a test to a group of students, below is the summary of grades by gender.

	a	b	c	total
female	4	9	6	19
total	22	17	13	52

if a student is randomly chosen, find the probability that the student is male or earned grade b. leave your answer as a reduced fraction.
question help: video

Explanation:

Step1: Recall probability formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of being male and $B$ is the event of getting grade B.

Step2: Calculate $P(A)$

The number of male students is $33$ and the total number of students is $52$. So $P(A)=\frac{33}{52}$.

Step3: Calculate $P(B)$

The number of students with grade B is $17$, so $P(B)=\frac{17}{52}$.

Step4: Calculate $P(A\cap B)$

The number of male students with grade B is $8$, so $P(A\cap B)=\frac{8}{52}$.

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{33}{52}+\frac{17}{52}-\frac{8}{52}=\frac{33 + 17- 8}{52}=\frac{42}{52}=\frac{21}{26}$.

Answer:

$\frac{21}{26}$