For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.88 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least oneof the 3 systems will detect it? 0.9959 Your answer should be rounded to 5 decimal places.

0.99827 = 99.827% probability that when a theft occurs, at least one of the 3 systems will detect it.

Step-by-step explanation:

For each system, there are only two possible outcomes. Either it detects the theft, or it does not. The probability of a system detecting a theft is independent of other systems. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

Each of the 3 systems detects theft with a probability of 0.88 independently of the others.

This means that

What is the probability that when a theft occurs, at least oneof the 3 systems will detect it?

0.99827 = 99.827% probability that when a theft occurs, at least one of the 3 systems will detect it.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

irrational, cannot