Question

giving a test to a group of students, the grades and gender are summarized below. round your answers to 4 decimal places. if one student is chosen at random, a. find the probability that the student got an a. 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 one student is chosen at random, find the probability that the student got a b given they are male.

	female	male	total
b	8	7	15
c	3	9	12
total	21	32	53

Explanation:

Step1: Recall probability formula

The probability of an event $E$ is $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of students is $53$.

Step2: Calculate probability for part a

The number of students who got an A is $26$. So $P(\text{got an A})=\frac{26}{53}\approx 0.4906$.

Step3: Calculate probability for part b

The number of male students who got a B is $7$. So $P(\text{male and got a B})=\frac{7}{53}\approx 0.1321$.

Step4: Calculate probability for part c

The number of female students or students who got an A: $n(\text{female or got an A})=n(\text{female})+n(\text{got an A})-n(\text{female and got an A})=21 + 26-10=37$. So $P(\text{female or got an A})=\frac{37}{53}\approx 0.6981$.

Step5: Calculate probability for part d

The number of male students is $32$, and the number of male students who got a B is $7$. So $P(\text{got a B}|\text{male})=\frac{7}{32}\approx 0.2188$.

Answer:

a. $0.4906$
b. $0.1321$
c. $0.6981$
d. $0.2188$