Question

PicnicTech markets three versions of its Picnic Egg Boxes: the Golden Deluxe, containing 3 gold eggs and one plain egg; the Regular, containing 2 gold and 2 plain; and the EconoLunch, containing just one gold egg and 3 plain ones. The corner store has 3 Golden Deluxes on sale, 2 Regulars, and 5 EconoLunches. This is all shown in the tree diagram below.

You go to the corner store and buy a Picnic Egg Box at random, and select an egg from it at random. The egg is gold! Use a probability tree diagram to calculate the probability that the box you bought was a Golden Deluxe.

A.9/40
B.9/20
C

Answer 1

C.3/4
D.1/2
E.11/20

Answer 2

oldie but goodie
http://openstudy.com/study#/updates/4de6fc564c0e8b0b6eb9b7d8

Answer 3

outstanding.

Answer 4

unfortunately on further inspection, this is not actually the question asked from you, is it?

Answer 5

we have to do some more work

Answer 6

lets put G = event you pick a gold egg, D as the event you pick from the deluxe box. then you are interested in finding \(P(D|G)\) the probability that you picked from deluxe box if your egg is gold

Answer 7

by definition \(P(D|G)=\frac{P(D\cap G)}{P(G)}\) and the numerator is easy, by the tree diagram it is \(\frac{3}{10}\times \frac{3}{4}=\frac{9}{40}\)

Answer 8

so you also need the probability you pick a gold egg (from whatever box) so you have to add up all the probabilities. if my calculations are correct (again from the tree diagram) it is
\[\frac{9}{40}+\frac{3}{20}+\frac{1}{8}=\frac{1}{2}\]

Answer 9

so your final answer is \[\frac{\frac{9}{40}}{\frac{1}{2}}=\frac{9}{40}\times 2=\frac{9}{20}\]

Answer 10

i hope this was one of the answers, and i also hope that i didn't make a calculation error, but you can check