Question

There is a 30 percent chance that A can fix her busted computer. If A cannot, then there is a 40 percent chance that her friend B can fix it.
a) Find the probability it will be fixed by either A or B.
b) If it is fixed, what is the probability it will be fixed by B.

Answer 1

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.