Mathematics, 23.09.2019 16:10 carterjpowell77

There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism. suppose a particular surveillance system has a 98% chance of correctly identifying a future terrorist and a 99.9% chance of correctly identifying someone who is not a future terrorist. if there are 1,000 future terrorists in a population of 300 million, and one of these 300 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist? (round your answer to six decimal places.)

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Given that a person was identified as a future terrorist, there is a 2.8544% probability that he/she actually is a future terrorist.

Step-by-step explanation:

There are 1000 future terrorists in a population of 300,000,000. So the probability that a randomly selected person in this population is a terrorist is:

$P = \frac{1,000}{300,000,000} = 0.000003 = 0.0003%$

So, we have these following probabilities:

A 99.9997% probability that a randomly chosen person is not a terrorist.

A 0.0003% probability that a randomly chosen person is a terrorist.

A 98% probability that a future terrorist is correctly identified

A 99.9% chance of correctly identifying someone who is not a future terrorist. This also means that there is a 0.01% probability of someone who is not a terrorist being identified as one.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

Here we have:

What is the probability that the person is a terrorist, given that she was identified as a terrorist.

P(B) is the probability that the person is a terrorist. So P(B) = 0.000003

P(A/B) is the probability that the person was identified as a terrorist, given that she is a terrorist. The problem states that the system has a 98% chance of correctly identifying a future terrorist, so P(A/B) = 0.98

P(A) is the probability of a person being a identified as a terrorist. So

$P(A) = P_{1} + P_{2}$

$P_{1}$ is the probability that a person is a terrorist and was identified as one. So:

$P_{1} = 0.000003*0.98 = 0.00000294$

$P_{1}$ is the probability that a person is not a terrorist and, but was identified as one. So:

$P_{2} = 0.999997*0.0001 = 0.0000999997$

$P(A) = P_{1} + P_{2} = 0.00000294 + 0.0000999997 = 0.000103$

The answer is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.000003*0.98}{0.000103} = 0.028544$

Given that a person was identified as a future terrorist, there is a 2.8544% probability that he/she actually is a future terrorist.

Answer from: Quest

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 2& 0& |8\\ 0& 0& 3& |9\end{bmatrix}$

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 1& 0& |4\\0& 0& 1& |3\end{bmatrix}$

What is the next step in solving this augmented matrix using gauss-jordan elimination method

Answer from: Quest

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without

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