Question

One fourth of the residents in Khalifa City leave their garaga door open when they are away from home. The local chief of police estimates that 5 percent of those 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 that the door was left open?

If a garage is not robbed, what is the probability that the door was closed?

Answer 1

Solution "onal wal # 5) let Al - Leave garage door open Ag = leave garage door closed. B : Something will be Stolen. Given PCA) = + +0.25 PCAO) = 3 = 0.45 P (B/A1) = 0.05 P (8/42] = 0.01 u jf garage is doobed, the probability that the door was left open is P(A/B). PCAT) PCBfA1) PCAI) PCB/41) + PC42) P (8/12) 0.25 x 0.05 (0.258005)+(0.45X0-01) 0.0125 b) It garage is that the door was closedis 0.0125 + 0.0015 = 0.625 not robbed, the probability PCA) PC8/12) plag) P(8/17) + P(42) P(B|A2) P (Ag/6) 0.45 x 0.01 (0.25 0.05)+(0-75X0:01) 0.0075 0.0125+0.045 = 0.375