SOLUTION: At a drug rehab center 35% experience depression and 28% experience weight gain. 14% experience both. If a patient from from the center is randomly selected, find the possibility

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Question 1182264: At a drug rehab center 35% experience depression and 28% experience weight gain.
14% experience both.
If a patient from from the center is randomly selected, find the possibility that the patient (Round to four decimals points 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.
_______

In a particular bag of skittles, there are 13 red, 12 orange, 10 green, 12 yellow, and 11 purple skittles.
Give the indicated probability as a fraction or w/o rounding.
1. Selecting a yellow skittle ________
2. Selecting a red or a purple skittle ________
3. Not selecting a green skittle _______
4. Selecting two consecutive orange skittles _______
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
At a drug rehab center 35% experience depression and 28% experience weight gain.
14% experience both.
If a patient from from the center is randomly selected, find the possibility that the patient (Round to four decimals points 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.

~~~~~~~~~~~~~~~~~~~~


                    I will solve problem  1,  ONLY. 


(a)   Experiences neither depression nor weight gain.


      P(neither A nor B) = 1 - (P(A) + P(B) - P(A and B)) = 1 - (0.35 + 0.28 - 0.14) = 0.51 = 51%.     ANSWER




(b)  Experiences depression given that the patient experiences weight gain.


     It is about finding the  CONDITIONAL probability


     P =  =  =  = 0.5 = 50%.    ANSWER.




(c)  Experiences weight gain given that the patient experiences depression.


     It is about finding the  CONDITIONAL probability, again.


     P =  =  =  =  =  = 0.4 = 40%.    ANSWER.

Solved.


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