Math Is Fun Forum

sptrae

Member

Registered: 2009-03-18

Posts: 1

Probability problem..Help please!

There is a problem and i cant get my head around it..any help would be much appeciated

In a general population the government know that a proportion p are
active terrorists. In conjunction with the secret services the government
scan email communications to decide whether an individual is a
terrorist or not (via a predictive test). From previous data the government
know that if an individual is indeed an active terrorist then the
test will give a positive response with chance 0.99. If an individual is
not a terrorist then the test will give a positive response with chance
0.001.

(a) Let p = 10−6. Suppose an individual is tested as positive for being
a terrorist. What is the probability that this individual is indeed
an active terrorist?

(b) Find the range of values of p for which there is a chance of at
least 50% that a suspect is an active terrorist given a positive test
response.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Probability problem..Help please!

The probability that an individual is tested positive is

Hence the probability that a positively tested individual is a terrorist is

Use this to answer both (a) and (b).