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.
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

Answer: a) $(0.99)^4$

Step-by-step explanation:

Given : 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 .

Probability for independent events $(E_1 , E_2 , E_3 , ....., E_n)$ occurs together =  $P(E_1)\times P(E_2)\times P(E_3)\ .....\times P(E_n)$.

Then, the probability that when a theft occurs, all four systems will detect it

= (0.99) x (0.99) x (0.99) x (0.99)

$= (0.99)^4$

Hence, the probability that when a theft occurs, all four systems will detect it is $(0.99)^4$ .

Hence, the correct answer is a) $(0.99)^4$ .