Grade Freshmen Sophomore Junior Senior A 0 8 9 10 B 0 6 8 11

Grade

Freshmen

Sophomore

Junior

Senior

A

0

8

9

10

B

0

6

8

11

C

1

7

9

12

D

2

4

1

4

F

0

6

2

1

TOTAL

3

31

29

38

What is the probability that the student is a junior and makes a B in the course?

What is the probability that the student does not make a A in the course, given that the student is a senior?

What is the probability that the student makes a 0 or F in the course?

Let A be the event that a sophomore is taking the course. Let B be the event that the student makes a C in the course. Are the events A and B independent? Are the events A and B mutually exclusive?

Solution

here total number of students=3+31+29+38=101

##P[student is junior and scores B]=(total juniors who scores B)/total students=8/101=0.0079 [answer]

##P[a student does not make A in the course given that the student is senior]=P[a senior does not make A]/P[student is a senior]=((38-10)/101)/(38/101)=28/38=0.73684 [answer]

##P[a student makes F]=total students make F/total students=(0+6+2+1)/101=0.08910 [answer]

##A be the event that a sophomore is taking the course. B be the event that the student makes C in the course.

so P[A]=31/101   P[B]=(1+7+9+12)/101=29/101

now P[AB]=P[a sopomore makes C]=7/101 which is not eual to P[A]*P[B]

so they are not independent

moreover P[AB] is not zero..so not mutually exclusive also.