SOLUTION: For safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 5 systems detects theft with a pr

Question 1123951: For safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 5 systems detects theft with a probability of 0.8 independently of the others.
The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. What is the probability that when a theft occurs, at least one of the 5 systems will detect it?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

For each single system of five, the probability that it will not detect a theft is  the complement  to 0.8,  i.e.  1-0.8 = 0.2.


The probability that NO ONE of five systems will detect a theft is  {{0.2^5}}} = 0.00032.


The probability that when a theft occurs, at least one of the 5 systems will detect it is THE COMPLEMENT to it,  i.e.  1 - 0.00032 = 0.99968.

Solved.

--------------------

For the collection of nice elementary problems on probability, see the lessons
    - Elementary Probability problems related to combinations
    - A True/False test
    - A shipment containing fair and defective alarm clocks
    - People in a room write down integer numbers at random
    - A drawer contains a mixture of socks
    - Students studying foreign languages
    - Probability for a computer to be damaged by viruses
    - Typical probability problems from the archive
    - Geometric probability problems
    - Advanced probability problems from the archive
    - Challenging probability problems
    - Selected probability problems from the archive
    - Unusual probability problems
    - Probability problem for the Day of April, 1
    - OVERVIEW of lessons on Probability
in this site.

Read them and have a fun !

                    H a p p y   l e a r n i n g ! !

RELATED QUESTIONS
For safety reasons, four different alarm systems were installed in the vault containing... (answered by math_helper)

For safety reasons, four different alarm systems were installed in the vault containing... (answered by jorel1380)

For safety reasons, the base of a 26 foot ladder should be at least 8 feet from the... (answered by jim_thompson5910)

For safety reasons, a rollercoaster at an amusement park has restrictions on the physical (answered by Theo)

The Highway Safety Institute conducted test crashes at 6 mph, calculating the costs for... (answered by stanbon)

For safety reasons, the manufacturer of a ladder recommends that it be used in such a way (answered by fractalier)

The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width (answered by stanbon,josmiceli)

5. Old-fashioned mechanical alarm clocks were not all that accurate. Suppose that the... (answered by ikleyn)

The Highway Safety Institute conducted test crashes at 6 mph, calculating the costs for... (answered by stanbon)