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# Probability question with conditional probability concepts

1) Presume there is a measure designed to detect depression in adolescents. This measure detects depression in people who truly are depressed 75% of the time (hit rate), but it diagnoses depression in those who are not truly depressed 20% of the time (false positive). Presume there exists a population of adolescents (infinite in size) to whom this measure will be given. In this population, 10% are truly depressed and 90% are not. Sampled randomly.

1a)What is the probability that the first individual to whom measure is given is not truly depressed if not diagnosed as depressed.

1b) What is the probability the measure makes a correct diagnosis. (think about what constitute a correct diagnosis, so not detecting something when there's nothing there would count as well)

1c) what is the probability the measure makes a correct diagnosis in exactly 3 of the first five cases.

#### Solution Preview

1) Presume there is a measure designed to detect depression in adolescents. This measure detects depression in people who truly are depressed 75% of the time (hit rate), but it diagnoses depression in those who are not truly depressed 20% of the time (false positive). Presume there exists a population of adolescents (infinite in size) to whom this measure will be given. In this population, 10% are truly depressed and 90% are not. Sampled randomly.

Probability that a person is depressed = 0.10
Probability that not depressed = 1 - 0.10 = 0.90
Probability that a person is diagnosed as depressed ...

#### Solution Summary

How to calculate conditional probabilities?
How to calculate binomial probability for k successes?

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