Chapter 5 Q32 Military Detection

Chapter 5 Q 32

Probability of one system detecting an attack is 0.9.

a. Probability of one system detecting an attack? 0.9 of course.

b. Probability of two systems installed in the same area and operating independently detecting an attack?

You could solve this using a tree diagram, but using binomials it like this: we have two trials because there are two systems, identical and independent. We want at least one success. That means we don’t want zero successes. So find the probability of zero successes and then subtract from 1. That will give us "at least one".

=binomdist(0,2,0.9, false) = 0.01

Then 1 – 0.01 = 0.99

c. Three systems is the same argument

=binomdist(0,3,0.99,false) = 0.001

Then 1 – 0.001 = 0.999

d. Would you recommend that multiple systems be used?

It would depend on the cost of extra systems and the likelihood of an attack in the first place. If the system is expensive and the risk of an attack is low, then the gain from 0.99 to 0.999 is very small compared to say, spending that money on better education for kids.

Testing for independence: probability

Q. If P(A) = 0.5, P(B) = 0.6 and P(A∩B)=0.3, test whether A and B are independent.

A. The test for independence is: if P(A|B) = P(A) then A and B are independent.

To run the test, we need to find P(A|B). We get this from P(A|B) = P(A∩B)/P(B).

Here that number is  0.3/0.6 = 0.5.

Now, is the correct? Does P(A|B) = P(A)? Yes because 0.5 = 0.5. So A and B are independent.