Kevin’s family has a history of diabetes. The probability that Kevin would inherit this disease is 0.75. Kevin decides to take a test to check if he has the disease. The accuracy of this test is 0.85. What is the probability that Kevin has diabetes and the test predicts this?.

To get the intersection of the both event you can simply multiply the both events because those two events are independent to each other so the formula would be (0.75) time (0.85) and the probability would be 0.6375. I hope you are satisfied with my answer and feel free to ask for more.

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-06-06T14:47:17+02:00

The probability that Kevin has diabetes and the test predicts this is 0.944.

What is Probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Here, Probability of Kevin have the disease P(D)= 0.75

Probability of Kevin does not have the disease P(D')= 0.25

Accuracy of test P(A) = 0.85

Failure of test P(A') = 0.15

Now, P(A/D) = [tex]\frac{P(A)P(D)}{P(A)P(D) + P(A')P(D')}[/tex]

[tex]P(\frac{A}{D} )= \frac{0.75 X 0.85}{0.75 X 0.85+0.25 X 0.15}[/tex]

[tex]P(\frac{A}{D}) = \frac{0.6375}{0.6375 + 0.0375}[/tex]

[tex]P(\frac{A}{D}) = 0.6375/0.675[/tex]

[tex]P(A/D) = 0.944[/tex]

Thus, the probability that Kevin has diabetes and the test predicts this is 0.944.

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