Question

giving a test to a group of students, the grades and gender are summarized below. round your answers to 4 decimal places.

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

if one student is chosen at random,
a. find the probability that the student got an a: 0.4906
b. find the probability that the student was male and got a \b\: 0.1148
c. find the probability that the student was female or got an \a\: 0.6981
d. if one student is chosen at random, find the probability that the student got an b given they are male.

Explanation:

Step1: Recall probability formula

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of students is $53$.

Step2: Calculate probability for part a

The number of students who got an A is $26$. So $P(\text{got an A})=\frac{26}{53}\approx0.4906$.

Step3: Calculate probability for part b

The number of male students who got a B is $7$. So $P(\text{male AND got a B})=\frac{7}{53}\approx0.1321$ (it seems there was a wrong - answer marked in the original for this part).

Step4: Calculate probability for part c

The number of female students or students who got an A: $n(\text{female}\cup\text{got an A})=n(\text{female})+n(\text{got an A})-n(\text{female AND got an A})=21 + 26-10=37$. So $P(\text{female OR got an A})=\frac{37}{53}\approx0.6981$.

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 $P(\text{got a B}|\text{male})=\frac{7}{32}\approx0.2188$.

Answer:

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