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 plain. Use a probability tree diagram to calculate the probability that the box you bought was a Golden Deluxe.

Answer 1

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Answer 2

In what follows, "g" stands for "gold", and "p" for plain.

Your experiment has a total of 3 + 2 + 5 = 10 outcomes. An outcome yields one of the following egg scenarios:

gggp with probability 3/10
ggpp with probability 2/10
gppp with probability 5/10

For each scenario we now consider the experiment of drawing an egg at random. The respective probabilities of drawing a plain one are 1/4 (for gggp), 2/4 (for ggpp), and 3/4 (for gppp). Thus, the probability of drawing a plain egg in the entire experiment is:

(3/10)*(1/4) + (2/10)*(2/4) + (5/10)*(3/4)

(I'll let you crunch the numbers yourself.)

Answer 3

thanks