[rajinairus]

Probabilities often come out differently than we would expect them to using common sense. This can occur when we have multipleevents, large numbers of individuals, and there are small probabilities involved. Here's an example.

In recent years we have learned that, for the purpose of finding terrorists, the National Security Agency (NSA) collects telephonerecords on all Americans making phone calls. If someone is suspected of being a terrorist or terrorist associate, based on the analysis
of these records, then they will be investigated much more closely. They will probably have their phone conversations recorded, theywill be followed everywhere, their financial records and tax returns will be investigated, and everything they do or have done will be
scrutinized by the government.

There are approximately 260,000,000 Americans who make phone calls. These would be people teen-age or older. And let’s say that the NSA system of analyzing their data is 99.99% accurate. This means that 99.99% of the time the NSA can correctly identify a
terrorist or terrorist associated person. And if a person is not a terrorist or associate, that is, they’re innocent, the NSA will get that right 99.99% of the time, too.

There probably aren’t very many terrorists or associates in the United States. But for our example we'll assume that there are 10,000 of these people. That’s a lot, but not really so many out of 260,000,000 people .

Regardless of what the NSA does, there is the chance that a mistake will be made. When the NSA investigates someone, they’re going to spend a lot of time and money and make that person’s life very difficult. So they don't want to be unnecessarily investigating a lotof innocent people. And when the NSA chooses NOT to investigate a person, they want to be really sure they haven’t missed someone who is a terrorist or associate.

Answer the following questions.
your answer to the requested number of decimal places – but use more in your calculation.
1. If a person is randomly selected, what is the probability that person is a terrorist or associate?

2. Of the 260,000,000 people, how many of them are terrorists or associates that the NSA misses? That is, the person is a terrorist or associate, but the NSA doesn’t investigate them. This is called a “false negative.”

3. If a person is randomly selected, what is the probability that the NSA will investigate that person? 7 decimal places.

4. If a person is randomly selected, what is the probability that the person is a terrorist or associate AND the NSA investigates that person?

5. Of the 260,000,000 people, how many of them are innocent people who will be investigated by the NSA? That is, the person is not a terrorist or associate, but the NSA investigates them anyway. This is called a “false positive.”

[ebaines]

Are you having trouble doing them yourself, or are you trying to make a point of some sort?

Question 3 can't be answered with the data you've provided, unless you assume that the NSA is sifting through every call by every single person.

By the way, much of the basic premise in your post is incorrect - however, that's a discussion better moved to the "politcs" or "Issues and causes" forums.