Question

In: Statistics and Probability

A home security system is designed to have a 99% reliability rate. Suppose that nine home...

A home security system is designed to have a 99% reliability rate. Suppose that nine home equipped with this system experience an attempted burglary. Find the probability that at least two of the alarms are triggered.

Group of answer choices

A) 1- (.01⁹ ) - 9* (.01⁸ )* (.99)

B) 1- (.99⁹ ) - 9* (.99⁸ )* (.01)

C) 1- (.99⁹ )

D) 1- (.01⁹ )

Solutions

Expert Solution

Answer:

Given that,

A home security system is designed to have a 99% reliability rate.

Suppose that nine homes equipped with this system experience an attempted burglary.

i.e,

n=9,

p=0.99

q=1-p

=1-0.99

=0.01

Find the probability that at least two of the alarms are triggered:

We know that,

X Bin(n, p)

P(At least 2)= P( X 2):

=1-P(X < 2)

=1-[P(X=0)+P(X=1)]

Answer: Option(A)

By continuing solving, we get

=1-[0.0000000000000000892]

=1-0

P( X 2) =1 (Approximately)

** Please comment on any doubt.

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orchestra answered 1 year ago

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