Mathematics: 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

Anew test has been devised for detecting a particular

giavanleer14

06.01.2022

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) = $\frac{\textup{1}}{\textup{100,000}}=0.00001$

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

= $\frac{P(p/c)\times P(C)}{P(p/c)\times P(C)+P(p/c')\times P(C')}$

= $\frac{0.95\times0.00001}{0.95\times0.00001+0.05\times0.99999}$

= 0.000189

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semily74

07.03.2022

Step-by-step explanation:

Factors of 27- 1, 3, 9, and 27

Factors of 63-1, 3, 7, 9, 21, 63

The Common factors are 3 and 9

The GCF is 9

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