Theoretical probability distribution example: multiplication  Probability & combinatorics  Summary and Q&A
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.
Questions & Answers
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.