Question

1.

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 0.82 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? Your answer should be rounded to 5 decimal places.

2.

An engineering school reports that 58% of its students were male (M), 39% of its students were between the ages of 18 and 20 (A), and that 32% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).

Your answer should be given to two decimal places.

Answer 1

(1)

The probability that when a theft occurs, at least one of the 3 systems will detect it = 1 - P(All 3 fail)

                                                                                                                        = 1 - (1 - 0.82)³

                                                                                                                          = 1 - 0.18³

                                                                                                                           = 1 - 0.005832

                                                                                                                          = 0.99417

So,

Answer is:

0.99417

(2)

From the given data, the following Table is calculated:

	between the ages of 18 and 20	Not between the ages of 18 and 20	Total
Male	0.32	0.26	0.58
Female	0.07	0.35	0.42
Total	0.39	0.61	1.00

P(Female OR between the ages of 18 and 20) = P(Female) + P( between the ages of 18 and 20) - P(Female AND between the ages of 18 and 20)

= 0.42 + 0.39 - 0.07

= 0.74

So,

Answer is:

0.74