Theoretical probability distribution example: multiplication | Probability & combinatorics | Summary and Q&A

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May 11, 2021
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Theoretical probability distribution example: multiplication | Probability & combinatorics

TL;DR

The video explains how to construct a theoretical probability distribution for the number of free desserts a customer might receive at a restaurant.

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Q: What does X represent in the context of the probability distribution?

X represents the number of free desserts Kai gets in his two visits to the restaurant. It can take on values from 0 to 2.

Q: Are the events of getting a free dessert on each visit independent?

Yes, the events of getting a free dessert on each visit are independent. The probability of getting a dessert on one visit does not affect the probability of getting one on the other visit.

Q: What is the probability of Kai not getting any free desserts?

The probability of Kai not getting any free desserts is 16/25. This is calculated by multiplying the probability of not getting a dessert on each day (4/5) together.

Q: What is the probability of Kai getting exactly one free dessert?

The probability of Kai getting exactly one free dessert is 8/25. This can happen in two scenarios: 1) not getting a dessert on day one and getting one on day two, or 2) getting a dessert on day one and not getting one on day two.

Q: What is the probability distribution for X?

The probability distribution for X is: X=0 with a probability of 16/25, X=1 with a probability of 8/25, and X=2 with a probability of 1/25.

Summary & Key Takeaways

• Kai visits a restaurant that has a promotion where 1 in 5 customers get a free dessert.

• X represents the number of free desserts Kai gets in his two visits.

• The probability distribution for X is: X=0 with a probability of 16/25, X=1 with a probability of 8/25, and X=2 with a probability of 1/25.