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 .99independently of the others.

Select one answer.
10 points
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. 4*(0.01)*(0.99)3
e. 4*(0.99)*(0.01)3

Answer 1

The probability that all four alarm systems will detect a theft when it occurs is the product of their individual probabilities, since each system operates independently of the others. Therefore, the probability is:

(.99)^4

This simplifies to:

0.96059601

Rounding to four decimal places, we get:

0.9606

So the answer is (a) (.99)^4, which is approximately 0.9606.