# 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.

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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

The expert determines how to calculate conditional probabilities. Calculates of the binomial probability for k successes are provided.

Probability problems related to empirical definition ,addition theorem, joint probability, marginal probability and conditional probability

A sample of 2,000 licensed drivers revealed the following number of speeding violations.

Number of Violations Number of Drivers

0 1,910

1 46

2 18

3 12

4 9

5 or more 5

Total 2,000

a. What is the experiment?

Testing the number of speeding violations per driver.

b. List one possible event.

46 drivers had one speeding violation.

c. What is the probability that a particular driver had exactly two speeding violations?

The probability that a particular driver had exactly two speeding violations is .009 found by 18/2000 = 0.009.

d. What concept of probability does this illustrate?

Empirical probability

Please check answers if they are correct ..if not please solve:

A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:

Major

Gender Accounting Management Finance Total

Male 100 150 50 300

Female 100 50 50 200

Total 200 200 100 500

a. What is the probability of selecting a female student?

P(F) = = 0.4

b. What is the probability of selecting a finance or accounting major?

c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?

P(Fm or A) = P(Fm) + P(A) - P (both Fm and A)

P(Fm or A) = 200/500 + 200/500 - 100/500

P(Fm or A) = .40 + .40 - .20

P(Fm or A) = .60

The probability of selecting a female or an accounting major is .60

Application used was Joint Probability.

d. Are gender and major independent? Why?

No because independence requires that P(A / B) = P(A)

In this case P(gender / major) = P(gender)

100/300 DOES NOT EQUAL 200/500

Joint Probability must be used

e. What is the probability of selecting an accounting major, given that the person selected is a male?

P(A and M) = P(A) P(M)

P(A and M) = = = .24

Probability of selecting an accounting major given the person selected is a male is .24.

f. Suppose two students are selected randomly to attend a lunch with the president of the university. What is the probability that both of those selected are accounting majors?

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