Mathematics: For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 4 systems detects theft with a probability of 0.86 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs,at least one of the 4 systems will detect it. what is the probability that when a theft occurs, at least oneof the 4 systems will detect it?

6/ 24 green 3/24 blue 2/24 yellow total 11/24 13/24 left which is white 13 * 2 = 26 white blue 4 *2 = 8...

For safety reasons, 4 different alarm systems

lily0806

06.01.2022

0.45299184

Step-by-step explanation:

Given : Number of different alarm systems were installed = 4

The probability that each of 4 systems detects theft : p = 0.86

Let x represents the number of security alarms that detects theft.

Binomial probability formula to find the probability of getting success in x trials= $P(x)=^nC_xp^n(1-p)^{n-x}$ , where n is total number of trials.

Now , the probability that when a theft occurs, at least one of the 4 systems will detect it will be:-

$P(x\geq1)=1-P(x=0)\\\\=1-^4C_0(0.86)^0(1-0.86)^{4}\\\\=1-(0.86)^4\\\\=1-0.54700816=0.45299184$

Hence, the probability that when a theft occurs, at least one of the 4 systems will detect it = 0.45299184

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