For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 4 systems detects theft with a probability of 0.86 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the 4 systems will detect it. what is the probability that when a theft occurs, at least oneof the 4 systems will detect it?

0.45299184

Step-by-step explanation:

Given : Number of different alarm systems were installed = 4

The probability that each of 4 systems detects theft : p = 0.86

Let x represents the number of security alarms that detects theft.

Binomial probability formula to find the probability of getting success in x trials= , where n is total number of trials.

Now , the probability that when a theft occurs, at least one of the 4 systems will detect it will be:-

Hence, the probability that when a theft occurs, at least one of the 4 systems will detect it = 0.45299184

step-by-step explanation: