Question

among a total of students, the grades and gender are summarized below. based your answers to 4
if a student is chosen at random,
a. find the probability that the student got an a: 0.4900
b. find the probability that the student was male and got a b.
c. find the probability that the student was female or got an a.
d. if a student is chosen at random, find the probability that the student got a b given they are male. 0.0911

Explanation:

Step1: Recall probability formula

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate probability of getting an A

The total number of students is $34 + 15+12=61$. The number of students who got an A is $34$. So $P(\text{got an A})=\frac{34}{61}\approx0.5574$.

Step3: Calculate probability of being male and getting a B

The number of male students who got a B is $7$. So $P(\text{male and got a B})=\frac{7}{61}\approx0.1148$.

Step4: Calculate probability of being female or getting an A

We use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event of being female and $B$ be the event of getting an A. The number of female students is $21$, number of students who got an A is $34$, and number of female students who got an A is $10$. So $P(\text{female})=\frac{21}{61}$, $P(\text{got an A})=\frac{34}{61}$, $P(\text{female and got an A})=\frac{10}{61}$. Then $P(\text{female or got an A})=\frac{21 + 34- 10}{61}=\frac{45}{61}\approx0.7377$.

Step5: Calculate probability of getting a B given male

We use the conditional - probability formula $P(B|A)=\frac{P(A\cap B)}{P(A)}$. Let $A$ be the event of being male and $B$ be the event of getting a B. The number of male students is $40$, and the number of male students who got a B is $7$. So $P(\text{got a B}|\text{male})=\frac{7}{40}=0.175$.

Answer:

The probabilities for parts a - d are approximately:
a. $0.5574$
b. $0.1148$
c. $0.7377$
d. $0.175$