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
[tex]\begin{gathered} \text{ = }\frac{p(D\text{ n W.G)}}{p(W\mathrm{}G)} \\ \text{ = }\frac{0.13}{0.29} \\ =0.448275 \\ =0.4483\text{ ( 4 decimal places)} \end{gathered}[/tex]
C.
Probability that the patient experience weight gain given that the patient expereince depression:
[tex]\begin{gathered} \text{ = }\frac{\text{p(W.G n D)}}{p(D)} \\ =\frac{0.13}{0.4} \\ =0.3250\text{ (4 decimal places)} \end{gathered}[/tex]
d.
No, depression and weight gain are not mutually exclusive
e.
No, depression and weight gain are not independent
