Question

The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings. If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling

Answer 1

The probability that two residential fires are in family homes, one is in an apartment, and one is in another type of dwelling is 0.07324 or 7.324%.

Step-by-step explanation:

To calculate the probability that two residential fires are in family homes, one is in an apartment, and one is in another type of dwelling, we will use the multiplication rule for independent events.

Let's assign the probabilities as follows:

P(family home) = 73% = 0.73

P(apartment) = 20% = 0.2

P(other type of dwelling) = 7% = 0.07

Now, we can calculate the probability:

P(two family homes, one apartment, one other dwelling) = P(family home) * P(family home) * P(apartment) * P(other type of dwelling)

= 0.73 * 0.73 * 0.2 * 0.07

= 0.07324

So, the probability that two residential fires are in family homes, one is in an apartment, and one is in another type of dwelling is approximately 0.07324 or 7.324%.