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

giving a test to a group of students, the grades and gender are summarized below. round your answers to 4 decimal places.\n| | female | male | total |\n|----|----|----|----|\n| a | 10 | 16 | 26 |\n| b | 8 | 7 | 15 |\n| c | 3 | 9 | 12 |\n| total | 21 | 32 | 53 |\nif one student is chosen at random,\n a. find the probability that the student got an a: 0.4906\n b. find the probability that the student was male and got a \b\: 0.1148\n c. find the probability that the student was female or got an \a\: 0.6981\n d. if one student is chosen at random, find the probability that the student got an b given they are male.

giving a test to a group of students, the grades and gender are summarized below. round your answers to 4 decimal places.\n| | female | male | total |\n|----|----|----|----|\n| a | 10 | 16 | 26 |\n| b | 8 | 7 | 15 |\n| c | 3 | 9 | 12 |\n| total | 21 | 32 | 53 |\nif one student is chosen at random,\n a. find the probability that the student got an a: 0.4906\n b. find the probability that the student was male and got a \b\: 0.1148\n c. find the probability that the student was female or got an \a\: 0.6981\n d. if one student is chosen at random, find the probability that the student got an b given they are male.

Answer

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. $0.2188$