You’re at a birthday party, and there are four bowls of snacks: Oreos, Doritos, Milk Duds and peanuts. You close your eyes and grab a bowl completely at random. Then you grab another bowl. What’s the probability that the two bowls you have drawn are the bowls with Oreos and Doritos?
There are two possible outcomes that can give us this result. The first is when you first get the bowl of Oreos and then the bowl of Doritos. The second is when you first get the bowl of Doritos and then the bowl of Oreos. You calculate the two probabilities separately:
Using the same procedure, you calculate the second probability:
Now you have to put the two parts together. The solution is to add the two probabilities together:
The probability of grabbing the bowls with Oreos and Doritos is
Notice that this probability is twice as high as the probabilities of grabbing the bowls in a given order such as first Oreos, then Doritos