Answer:
(a) 0.70
(b) 0.40
Step-by-step explanation:
Mutually-exclusive events are those events which cannot occur together.
Consider that events X and Y are mutually exclusive.
P (X and Y) = 0
Here the two events can be defined as follows:
A = A can fix the busted computer
B = B can fix the busted computer
The information provided are as follows:
P (A) = 0.30
P (B) = 0.40
If A cannot, then there is a chance that her friend B can fix it.
The above statement suggest that the events A and B are mutually exclusive, i.e. if A can fix the computer then B does not have to and if cannot then only B will fix it.
That is, P (A and B) = 0.
(a)
Compute the probability it will be fixed by either A or B as follows:
P (A or B) = P (A) + P (B) - P (A and B)
= 0.30 + 0.40 - 0
= 0.70
Thus, the probability it will be fixed by either A or B is 0.70.
(b)
Compute the probability that if it is fixed it will be fixed by B as follows:
P (not A and B) = P (B) - P (A and B)
= 0.40 - 0
= 0.40
Thus, the probability that if it is fixed it will be fixed by B is 0.40.
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, then the expression becomes: