Comparing Probabilities: Union and Intersection of Events

The video tutorial explains the probability concepts of union and intersection using a lucky envelope game. It begins with an introduction to the problem, followed by a detailed explanation of intersection and union using Venn diagrams. The tutorial then calculates the probabilities of selecting red and lucky envelopes, and compares the probabilities of union and intersection. The lesson concludes by reinforcing the understanding of these concepts through a two-way table.

What is the main question posed in the introduction regarding the envelopes?

• How many envelopes are there in total?

• What is the probability of selecting a blue envelope?

• How do the probabilities of selecting a red or lucky envelope compare to selecting a red lucky envelope?

• What is the value of the bill in the lucky envelopes?

In the context of a Venn diagram, what does the intersection represent?

• The difference between two sets

• The total number of events

• The overlapping region of two sets

• The union of all sets

How is the probability of the union of two events calculated?

• By adding the probabilities of each event and subtracting the intersection

• By adding the probabilities of each event

• By multiplying the probabilities of each event

• By subtracting the probabilities of each event

In the lucky envelope game, what is the probability of selecting a red and lucky envelope?

• 25%

• 50%

• 100%

• 75%

Why is the probability of union always greater than or equal to the probability of intersection?

• Because intersection is a subset of union

• Because union includes all possible outcomes

• Because intersection is always zero

• Because union is calculated by multiplying probabilities