Question

A student’s score on an exam is an integer between 0 and 100. A score of 90 to 100 is an A, 80 to 89 is a B, 70 to 79 is a C, 60 to 69 is a D, and below 60 is a failing grade of F. It is known that scores between 51 and 100 are equally likely and scores less than 50 cannot occur. Find the following probabilities: (a) Find the probability the student gets an A? (b) Find the probability that student fails the exam. (c) Find the probability that the student who is known not to have a C grade, has a B grade. (d) Find the probability that a student who is known to have passed the course, has a B grade.

Answer 1

Answer:

A. 0.22

B. 0.18

C. 0.25

D. 0.244

Step-by-step explanation:

S = {51 to 100} = 50

The sample space S contains values from 51 to 100 which is a total of 50 different values.

A.

Probability of A (lies between the values of 90 to 100 = 11).

11/50 = 0.22

B.

For a student to fail the course, his course has to be less than 60 = from 51 to 59. A total of 9 values.

9/50 = 0.18

C.

For student to get c, (70 to 79) a total of 10 values: 10/50 = 0.20

P(student did not get C) = 1-0.20 = 0.80

To get B, ( 80 to 89)

10/50 = 0.20

Probability that a student who is known not to have a c grade has a b grade = 0.20/0.80 = 0.25

D.

Probability of passing lies between 60 to 100 = 41 scores

41/50 = 0.82

Probability of student who passed having a B = 0.20/0.82 = 0.244