ACT Math : Probability
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Example Question #91 : Probability
There are 42 candies in a jar. One-third of the candies are chocolate, one-sixth of the candies are caramel and one-sixth of candies are coconut. The rest of the candies are mint. If you select three pieces of candy from the jar, what is the approximate probability that two are chocolate and one is coconut?
2.2%
16.7%
3.5%
1.8%
5.5%
5.5%
Total Chocolates = 1/3 * 42 = 14
Total Coconuts = 1/6 * 42 = 7
There are 14 chocolates and 7 coconuts to choose from 42 total candies, and note that each time you select one candy, the total number of candies decreases by one.
So assume that to arrive at the desired outcome of two chocolate and one coconut, you chose two chocolates and then a coconut. After picking out the first chocolate, there are now 13 chocolates to choose from 41 total candies. And after picking out the second chocolate, that leaves 7 coconuts to choose from 40 total candies.
The probability of that outcome = (14/42)(13/41)(7/40) = 0.01849, or just under 1.85%
However, there are two other sequences that could arrive at that desired outcome: chocolate, coconut, chocolate (which would be 14/42 * 7/41 * 13/40 = 1.85%) and coconut, chocolate, chocolate (which would be 7/42 * 14/41 * 13/40 = 1.85%). So summing all three probabilities of favorable outcomes gives you approximately 5.5%
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