For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the four systems detects theft with a probability of 0.99 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. what is the probability that when a theft occurs, at least one of the four systems will detect it. this probability is equal to: (a) (.99)4(b) (.01)4(c) 1- (.99)4(d) 1- (.01)4(e) 1- (.01)*4

The probability that at least one of the four systems will detect it is .

Step-by-step explanation:

Consider the provided information.

Each of the four systems detects theft with a probability of 0.99 independently of the others.

Systems detects theft = p = 0.99

Systems fail to detects theft = q = 1-0.99=0.01

We need to find the probability that when a theft occurs, at least one of the four systems will detect it.

Pr (at least 1 systems detect theft) = 1 - Pr (none of the systems detect theft)

Pr (at least one systems detect theft =

Pr (at least one systems detect theft =

Hence, the probability that at least one of the four systems will detect it is .

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42