Question

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.

Answer 1

`0.99^4`

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 =
`P(A) * P(B) * P(C) * P(D) = 0.99^4`

Hence The probability that when a theft occurs, all four systems will detect it is
`0.99^4`