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

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.