Question

At a drug rehab center 40% experience depression and 29% experience weight gain. 13%experience bothif a patient from the center is randomly selected, find the probability that the patient (Round allanswers to four decimal places where possible)a experiences neither depression nor weight gainb. experiences depression, given that the patient experiences weight gain.C. experiences weight gain, given that the patient experiences depressiond. Are depression and weight gain mutually exclusive?O noO yese Are depression and weight gain independent?o yesno

Answer 1

Percentage of patients experiencing depression = 40% = 0.4

Percentage of patients experiencing weight gain = 29% = 0.29

Percentage of patients experiencing both= 13% = 0.13

Probability that the patient

a. expereience neither depression nor weight gain:

x + 0.27 + 0.13 + 0.16 = 1

Probability that the patient

a. expereience neither depression nor weight gain:

x + 0.56 = 1

x= 1 - 0.56

x = 0.4400 ( 4 decimal places)

Probability that the patient expereience neither depression nor weight gain = 0.4400

b. Probability that the patient experience depression given that the patient expereince weight gain:

Let D represent Depression, W.G represents Weight gain

`\begin{gathered} \text{ = }\frac{p(D\text{ n W.G)}}{p(W\mathrm{}G)} \\ \text{ = }(0.13)/(0.29) \\ =0.448275 \\ =0.4483\text{ ( 4 decimal places)} \end{gathered}`

C.

Probability that the patient experience weight gain given that the patient expereince depression:

`\begin{gathered} \text{ = }\frac{\text{p(W.G n D)}}{p(D)} \\ =(0.13)/(0.4) \\ =0.3250\text{ (4 decimal places)} \end{gathered}`

d.

No, depression and weight gain are not mutually exclusive

e.

No, depression and weight gain are not independent