Asked Feb 24, 2020

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)


Expert Answer

Step 1

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

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

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...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: A pharmaceutical company receives large shipments of ibuprofen tablets and uses this acceptance samp...

A: From the given information, the percent of defects is 4% and the number of tablets is 23. The shipme...


Q: The mean IQ score of the students enrolled in University X is 100 and the standard iation is 16.1 A)...

A: Consider X be a random variable which follows normal distribution indicates the IQ scores of the stu...


Q: 0.54 0.55 0.58 0.61 0.66 0.66 0.67 0.68 0.77 Construct a stem-and-leaf display using repeated stems....

A: The stem and leaf display is given as:


Q: For the following studies, identify the population, sample, population parameter, and smaple statist...

A: The population can be defined as the cluster of all the individuals whose characteristics a research...


Q: In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are sele...

A: Consider X be random variable which follows binomial distribution indicates the students belongs to ...


Q: how do you solve a probability? In a certain​ lottery, you must correctly select 5 numbers​ (in an...

A: Number of ways of selecting 5 numbers out of 38 is given by


Q: 3. True or False? A linear regression equation and multiple linear regression equations can be used ...

A: A linear regression applies when there is one dependent variable and one independent variable while ...


Q: Using data set G, answer the questions given below.  DATA SET G Mileage and Vehicle Weight(n = 73...

A: (b)   Let us consider City MPG as dependent variable(Y) and Weight as independent variable(X).   Exc...


Q: 5. A. Draw a bell-shaped curve and label the axis with the 7 values including the mean of 500 in the...

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...