Question

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 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If a garage is robbed, what is the probability the doors were left open?

Answer 1

0.625 or 62.5 %

Explanation:

Calculation to find the probability that the doors were left open

First step is to find the probabilities of doors open and robbed

Probability of door open and robbed =

(25/100)*(5/100)

Probability of door open and robbed= 0.25*0.05

Probability of door open and robbed=0.0125

Second step is to find the probabilities of doors closed and robbed

Probability of door closed and robbed=

(75/100)*(1/100)

Note that 3/4 will give us 75%

Probability of door closed and robbed=0.75*0.01

Probability of door closed and robbed=0.0075

Third step is to find the probability of getting robbed

Probability of getting robbed =0.0075+0.0125

Probability of getting robbed=0.02

Last step is to find the probability that the doors were left open

Using this formula

Probability of open doors = P[door open & robbed] / P[robbed]

Let plug in the formula

Probability of open doors= 0.0125/0.02

Probability of open doors=0.625*100

Probability of open doors=62.5 %

Therefore the probability that the doors were left open will be 0.625 or 62.5 %