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### Course: AP®︎/College Statistics>Unit 8

Lesson 1: Introduction to random variables and probability distributions

# Theoretical probability distribution example: multiplication

We can create a probability distribution for the number of times someone wins a prize using the multiplication rule. Created by Sal Khan.

## Want to join the conversation?

• Why 4? Where does the 4 comes from?
• Each time Kai goes to the restaurant there are two possible outcomes:
either he gets a free dessert, or he doesn't get a free dessert.

The probabilities of these two outcomes must add up to 1.
So, if the probability that Kai gets a free dessert is 1∕5,
then the probability that he doesn't get a free dessert is 4∕5.
• Could you please explain me why Sal add up (and not multiply) the probabilities of 2 scenarii of the 2nd option (P(X=1))? (It starts at )
• A bit late, but for people with the same question:

Think about the fact that the probability of getting a single pie involves two different scenarios:
1. You get pie only the first day
2. You get pie only the second day

For calculating each of these two, you have to use the multiplication principle. In the first case, you multiply the probability of getting pie the first day (`1/5`) and the probability of not getting the pie the second day (`4/5`), which gives `4/25`. The reasoning is the same for the second day.

The reason why you add these two is that you're calculating the theoretical probability distribution, and you have to consider all cases. As I said earlier, getting a single pie involve these two different scenarios, so calculating the probability for this event means you have to add them (`4/25 + 4/25 = 8/25`). And it makes sense because adding all the probabilities together gives us 1.

PD: the plural of "scenario" is simply "scenarios". "scenarii" is incorrect, and that only applies to word derived directly from Latin (such as radius/radii, or cactus/cacti)
• Why the number 4? Where did it come from?