Two buildings are located close together at a production facility.The probability that either of these buildings will experience a fire loss is 4 percent.However,if one building has a fire,the probability that the second building will have a fire is 60 percent.What is the probability that both buildings will have a fire?
A)1)6 percent
B)2)4 percent
C)8)0 percent
D)64.0 percent

Question

Quizplus · Accepted Answer

The probability of both buildings having a fire can be calculated using the formula for conditional probability:

P(A and B) = P(A) x P(B given A)

Where A and B are events, P(A) is the probability of event A occurring, and P(B given A) is the probability of event B occurring given that event A has already occurred.

In this case, let A be the event that one building has a fire and B be the event that the other building has a fire. The probability of event A occurring is 4 percent, or 0.04. If event A occurs, the probability of event B occurring is 60 percent, or 0.6. Therefore:

P(A and B) = P(A) x P(B given A) = 0.04 x 0.6 = 0.024 or 2.4 percent.

So the probability that both buildings will have a fire is 2.4 percent, or closest to choice B) 2) 4 percent.

Two Buildings Are Located Close Together at a Production Facility