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.
You go to the corner store and buy a Picnic Egg Box at random, and select an egg from it at random. Use a probability tree diagram to calculate the probability that the egg is a gold one.
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prob = num of gold eggs/total num of eggs
each box has 4 eggs->40 total eggs
deluxe has 3 gold eggs: 3*3=9
regular has 2 gold eggs: 2*2=4
econo has 1 gold egg: 1*5 =5
-> 18 total gold eggs
P(egg is gold) = 18/40 = 9/20
the answer is 1/4 my teacher gave me this answer
i disagree, if you draw out a probability tree diagram you will see that 12 branches come from choosing a golden deluxe box and 9 of those result in a golden egg. 8 branches come from choosing a regular box and 4 result in a golden egg. 20 branches come from choosing an economy box and only 5 result in a golden egg.
Number of branches resulting in golden egg: 9+4+5 = 18
Total branches or possible outcomes: 12+8+20 = 40
Probability = 18/40 = 9/20
You have a 45% chance of getting a golden egg