Mathematics, 18.03.2020 23:05 clinky89

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.

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Answer from: adeline12401

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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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 n = 3, p = 0.88

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

$P(X \geq 1) = P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{3,1}.(0.88)^{1}.(0.12)^{2} = 0.03802$

$P(X = 2) = C_{3,2}.(0.88)^{2}.(0.12)^{1} = 0.27878$

$P(X = 3) = C_{3,3}.(0.88)^{3}.(0.12)^{0} = 0.68147$

$P(X \geq 1) = P(X = 1) + P(X = 2) + P(X = 3) = 0.03802 + 0.27878 + 0.68147 = 0.99827$

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

Answer from: Quest

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

Answer from: Quest

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

$3x-6$

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

$3x-6=0$

$3x=6$

$x=\frac{6}{3}=2$

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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