Question
Asked Feb 24, 2020
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At a drug rehab center 38% experience depression and 29% experience weight gain. 11% experience both. If a patient from the center is randomly selected, find the probability that the patient (Round all answers to four decimal places where possible.)

a. experiences neither depression nor weight gain.  

b. experiences depression given that the patient experiences weight gain.

c. experiences weight gain given that the patient experiences depression.  (round to 4 decimal places)

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Expert Answer

Step 1

Given
percentage of patients experience depression = 38%
percentage of patients experience weight gain = 29%
percentage of patients experience both = 11%

a)
The probability of patients experience depression = 0.38
The probability of patients experience weight gain = 0.29
The probability of patients experience both = 0.11

The probability that patients experience either depression or weight gain = P(depression) + P(weight gain) - P(depression and weight gain) = 0.38+0.29 - 0.11 = 0.56

The probability that patients experiences neither depression nor weight gain = 1 - P(depression or weight gain) = 1 - 0.56 = 0.44

Step 2

b)
Let Probability that patient experiences depression = P(D)
Probability that patient experiences weight gain = P(W)
The probability that patient experiences depression given that the patient experiences weight gain is calculated as shown below.
Statistics homework question answer, step 2, image 1

The probability that patient experiences depression given that the patient expe...

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