Question

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%

Answer 1

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%