Answer:
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.
