Jane is taking two courses. The probablity she passes the first course is 0,7. The probablity she passes the second course is 0.8. The probablity she passes at least one of the courses is 0.9. a. What is the probability she passes both courses? Give your answer to two decimall places b. Is the event she passes one course independent of the event that she passes the other course? True False c. What is the probability she does not pass either course (has two failing grades) ? Give your answer to two decimal places d. what is the probability she does not pass both courses (does not have two passing grades) ? Give your answer to two decimal places e. What is the probability she passes exactly one course?

a. 0.6

b. not independent

c. 0.1

d. 0.4

e. 0.3

Step-by-step explanation:

a.

P (passing first course) = P (C1) = 0.7

P (passing second course) = P (C2) = 0.8

P (passing at least one course) = P (C1∪C2) = 0.9

P (passes both courses) = P (C1∩C2) = ?

We know that

P (A∪B) = P (A) + P (B) - P (A∩B)

P (A∩B) = P (A) + P (B) - P (A∪B)

So,

P (passes both courses) = P (C1∩C2) = P (C1) + P (C2) - P (C1∪C2)

P (passes both courses) = P (C1∩C2) = 0.7+0.8-0.9

P (passes both courses) = P (C1∩C2) = 0.6

Thus, the probability she passes both courses is 0.6.

b.

The event of passing one course is independent of passing another course if

P (C1∩C2) = P (C1) * P (C2)

P (C1) * P (C2) = 0.7*0.8=0.56

P (C1∩C2) = 0.6

As,

0.6≠0.56

P (C1∩C2) ≠P (C1) * P (C2),

So, the event of passing one course is dependent of passing another course.

c.

P (not passing either course) = P (C1∪C2) '=1-P (C1∪C2)

P (not passing either course) = P (C1∪C2) '=1-0.9

P (not passing either course) = P (C1∪C2) '=0.1

Thus, the probability of not passing either course is 0.1.

d.

P (not passing both courses) = P (C1∩C2) '=1-P (C1∩C2)

P (not passing both courses) = P (C1∩C2) '=1-0.6

P (not passing both courses) = P (C1∩C2) '=0.4

Thus, the probability of not passing both courses is 0.4.

e.

P (passing exactly one course) = ?

P (passing exactly course 1) = P (C1) - P (C1∩C2) = 0.7-0.6=0.1

P (passing exactly course 2) = P (C2) - P (C1∩C2) = 0.8-0.6=0.2

P (passing exactly one course) = P (passing exactly course 1) + P (passing exactly course 2)

P (passing exactly one course) = 0.1+0.2

P (passing exactly one course) = 0.3

Thus, the probability of passing exactly one course is 0.3.