Question

40. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in the course. A student is chosen at random from the class. a. Find the probability that the student is a woman. b. Find the probability that the student received an A. c. Find the probability that the student is a woman or received an A. d. Find the probability that the student did not receive an A.

Answer 1

a) 56.67% probability that the student is a woman

b) 16.67% probability that the student received an A

c) 63.33% probability that the student is a woman or received an A.

d) 83.33% probability that the student did not receive an A.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have that:

30 students

13 men

17 women

2 men that got an A and 11 men that did not get an A.

3 women that got an A and 14 women that did not get an A.

a. Find the probability that the student is a woman.

30 students, of which 17 are women.

`P = (17)/(30) = 0.5667`

56.67% probability that the student is a woman

b. Find the probability that the student received an A.

30 students, of which 5 received an A

`P = (5)/(30) = 0.1667`

16.67% probability that the student received an A

c. Find the probability that the student is a woman or received an A.

30 students, of which 17 are women and 2 are men who received an A. So

`P = (19)/(30) = 0.6333`

63.33% probability that the student is a woman or received an A.

d. Find the probability that the student did not receive an A.

30 students, of which 25 did not receive an A.

`P = (25)/(30) = 0.8333`

83.33% probability that the student did not receive an A.