Question

A large bank vault has several automatic burglar alarms. The probability is 0.55 that a single alarm will detect a burglar. (a) how many such alarms should be used to be 99% certain that a burglar trying to enter is detected by at least one alarm?

Answer 1

Thank you for asking this question. Here is your answer:

Define X as the number of alarms that detect a burglar trying to enter given that there are n alarms.

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.5500.45n = 1 - 0.45n = 0.99

0.45n = 0.01

nlog(0.45) = log(0.01)

n = log(0.01) / log(0.45) = 5.8

Therefore 6 alarms are needed.

If the bank install 9 alarms, what is the expected number of alarms that will detect a burglar?

9(0.55) = 4.95

If there is any confusion please leave a comment below.