Question

Help!
At the Student Center cafeteria, 20% of those eating lunch are on a diet and 80% are not. Of those on a diet, 90% select a low-fat dessert, and 20% of those not on a diet select a low-fat dessert. Find the probability that a person who selects a low-fat dessert is on a diet.

Answer 1

I found 9/17, @sourwing what do you think?

Answer 2

how did you get that?

Answer 3

Did you draw a tree diagram?

Answer 4

diet and low-fat = 20% * 90% = 0.18
no diet and low-fat = 80% * 80% = 0.16
total of low-fat is 0.18+0.16=0.34
P(diet)=0.18/0.34

Answer 5

Yes I tried drawing the tree diagram but I really don't understand it..

Answer 6

Thanks @lucaz =)

Answer 7

so you're good?

Answer 8

For this question yes,but for the rest of the questions it requires drawing a tree diagram.. Could you explain to me how the tree diagram works? I get confuse on where to place the information that is provided in the question.

Answer 9

So you're finding P(D | LFD) yes?

Answer 10

D = diet
LFD = low fat dessert
ND = not diet
NLFD = not low fat dessert

Answer 11

using conditional probability formula:
P(D | LFD) = P(D and LFD) / P(LFD)

Answer 12

P(LFD) = P(D and LFD) + P(ND + LFD) = (0.2)(0.9) + (0.8)(0.2)
and P(D and LFD) = (0.2)(0.9)

so,
P(D | LFD) = (0.2)(0.9) / [(0.2)(0.9) + (0.8)(0.2)]
= 9/17

Answer 13

Ok, thank you for explaining =)