The National Institute of Mental Health reports that there is a 20% chance of an
ID: 3241295 • Letter: T
Question
The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Three randomly selected adult Americans are examined for psychiatric disorders. Let a success correspond to an adult American having a psychiatric disorder. a. Complete the following table. S represents success, an adult American has a psychiatric disorder
and f represents failure, an adult American does not have a psychiatric disorder. Display the probabilities to four decimal places.
Use the table you created above to answer the following questions
b. What is the probability the first person selected has a psychiatric disorder, but the second and third do not?
c. What is the probability that exactly one of the three people have a psychiatric disorder?
d. If X is the number of adult Americans with a psychiatric disorder in a sample of 3, complete the following probability distribution, using your answers to the questions above.
Outcome Probability sss ssfExplanation / Answer
P(S) = 0.2
P(F) = 0.8
a)
b) P(first person selected has a psychiatric disorder, but the second and third do not) = P(SFF) = 0.128
c) P(exactly one of the three people have a psychiatric disorder) = 0.128 + 0.128 + 0.128
= 0.384
d)
Outcome Probability SSS 0.2x0.2x0.2 = 0.008 SSF 0.2x0.2x0.8 = 0.032 SFS 0.032 FSS 0.032 SFF 0.2x0.8x0.8 = 0.128 FSF 0.128 FFS 0.128 FFF 0.8x0.8x0.8 = 0.512Related Questions
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