Exploring Compound Sample Space Concepts

The video tutorial explains the concept of sample space and compound events. It begins with an introduction to sample space, using a spinner and a coin to demonstrate simple and compound events. A tree diagram is used to illustrate how to calculate possible outcomes for compound events. The tutorial then shows how to build a table to represent outcomes when using a die, and finally, it demonstrates listing outcomes using clothing combinations. The video emphasizes understanding the multiplication of outcomes to determine the total number of possible outcomes in compound events.

What defines a compound sample space?

• A space with only one possible outcome

• An event that cannot be predicted

• An event with multiple outcomes

• Combining two separate events into one

What is the difference between simple and compound sample spaces?

• Simple spaces involve one event, compound involve multiple events

• Simple spaces have unlimited outcomes, compound have limited

• Compound spaces can be predicted, simple cannot

• There is no difference

How many outcomes are possible with a spinner (red, green, blue) and a coin (heads, tails)?

• 12

• 2

• 6

• 3

What is the purpose of using a tree diagram in compound sample spaces?

• To calculate probabilities

• To list all possible outcomes

• To show relationships between events

• Both A and C

In the spinner and coin example, what is one possible outcome?

• Green tail

• Blue head

• Red head

• All of the above

When combining a spinner with a die, how many total outcomes are possible?

• 6

• 18

• 36

• 3

How do you calculate the total number of outcomes in a compound sample space?

• By multiplying the number of outcomes for each event

• By dividing the outcomes of one event by the other

• By subtracting the outcomes of one event from the other

• By adding the number of outcomes for each event

Why do we multiply the outcomes of each event in a compound sample space?

• To find the maximum possible outcome

• To determine the least likely outcome

• To calculate the total number of possible outcomes

• To identify the most likely outcome

What combination is possible from the clothing example?

• Orange jeans, pink hat, blue shirt

• Pink shirt, blue jeans, white hat

• Red hat, yellow shirt, green jeans

• Blue jeans, green shirt, orange hat

How many total outfits are possible from the given clothing options?

• 18

• 12

• 6

• 24