One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 % of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If the garage is robbed, what is the probability the doors ware left open

If the garage is robbed, the probability the doors ware left open is 0.625.

Step-by-step explanation:

Denote the events as follows:

X = garage doors open

Y = something is stolen

The information provided is:

P (X) = 0.25

P (Y|X) = 0.05

P (Y|X') = 0.01

Compute probability that the garage is robbed as follows:

Compute the probability the doors ware left open given that the garage is robbed as follows:

Thus, if the garage is robbed, the probability the doors ware left open is 0.625.

the nearest power is 1.651.

means 7482 to the 1.651th power is almost equal to 2489287