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 .99 independently of the others.

1.) what is the probability that when a theft occurs, all four systems will detect it?

(a) (.99)4
(b) (.99) * 4
(c) (.01)4
(d) (.01) * 4
(e) none of the above.

Step-by-step explanation:

We are given Each of the four systems detects theft with a probability of .99 independently of the others.

Let the four systems be A , B , C and D

Probability of detecting theft by A = 0.99

Probability of detecting theft by B = 0.99

Probability of detecting theft by C = 0.99

Probability of detecting theft by D = 0.99

Since A , B , C and D  are independent

So,The probability that when a theft occurs, all four systems will detect it =

Hence The probability that when a theft occurs, all four systems will detect it  is

69.64%

step-by-step explanation: