Anew test has been devised for detecting a particular type of cancer. if the test is applied to a person who has this type of cancer, the probability that the person will have a positive reaction is 0.95 and the probability that the person will have a negative reaction is 0.05. if the test is applied to a person who does not have this type of cancer, the probability that the person will have a positive reaction is 0.05 and the probability that the person will have a negative reaction is 0.95. suppose that in the general population, one person out of every 100,000 people has this type of cancer. if a person selected at random has a positive reaction to the test, what is the probability that he has this type of cancer?

0.000189

Step-by-step explanation:

Given:

Probability of positive reaction given that he has cancer, P(p/c) = 0.95

Probability of negative reaction given that he has cancer, P(n/c) = 0.05

Probability of positive reaction given that not having cancer, P(p/c') = 0.05

Probability of negative reaction given that not having cancer, P(n/c') = 0.95

Probability that the person has particular type of cancer,

P(C) =

Probability that the person does not has particular type of cancer,

P(C') = 1 - 0.00001 = 0.99999

Now,

Using the Baye's Theorem

Probability that the person selected at random has a positive reaction to the test, that he has this type of cancer

=

=  

= 0.000189

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

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