Question

In: Statistics and Probability

A certain genetic mutation occurs in 5% of the population of Whoville. The mutation causes otherwise...

A certain genetic mutation occurs in 5% of the population of Whoville. The mutation causes otherwise normal adult Whos to grow green tail feathers during full moons. A test for this mutation has a sensitivity of 95% and a specificity of 98%. This means that the probability that a Who with the mutation tests positive is 95%, and the probability that a Who without the mutation tests positive is 100%-98%=2%.

If a random adult Who is tested for the mutation, then the probability of a positive result is

Group of answer choices

13.56%

6.65%

5%

95%

If a randomly selected Who tests positive for the mutation, then the probability that this Who actually has the mutation is

Group of answer choices

70.8%

5%

71.43%

95%

Expert Solution

Let

M=event that a randomly selected Who has the genetic mutation
NM=event that a randomly selected Who does not have the genetic mutation
T+=event that any given test is postive
T-=event that any given test is negative

A certain genetic mutation occurs in 5% of the population of Whoville. This is same as the probability that a randomly selected Who has the mutation is 0.05

P(M)=0.05

the probability that a randomly selected Who does not have the mutation is

P(NM) = 1- P(M) =1-0.05 = 0.95

The mutation causes otherwise normal adult Whos to grow green tail feathers during full moons. A test for this mutation has a sensitivity of 95% and a specificity of 98%.

This means that the probability that a Who with the mutation tests positive is 95%,

and the probability that a Who without the mutation tests positive is 100%-98%=2%.

If a random adult Who is tested for the mutation, then the probability of a positive result is

If a random adult Who is tested for the mutation, then the probability of a positive result is 0.0665

ans: 6.65%

If a randomly selected Who tests positive for the mutation, then the probability that this Who actually has the mutation is

If a randomly selected Who tests positive for the mutation, then the probability that this Who actually has the mutation is 0.7143

ans: 71.43%

orchestra answered 2 years ago

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