Exploring Probability in Compound Sample Spaces

The video tutorial explains a game show scenario where participants choose a vacation. It introduces the concept of sample space using a grid to list possible vacation outcomes. The tutorial then calculates the probability of selecting a vacation without snow for at least two days, assuming all outcomes are equally likely. The probability is determined by identifying outcomes that meet the criteria and dividing by the total number of outcomes.

What are the three possible types of vacations you can choose from in the game show?

• Island beach vacation, Ski vacation, City tour

• Island beach vacation, City tour, Camping

• City tour, Ski vacation, Camping

• Island beach vacation, Ski vacation, Camping

How many days can you choose to go on a vacation?

• Two, Three, or Four days

• One, Two, or Four days

• One, Two, or Three days

• One, Three, or Four days

What is the term used to describe all possible outcomes of the vacation choices?

• Outcome space

• Probability space

• Event space

• Sample space

How many total outcomes are there in the sample space for the vacation choices?

• Three

• Nine

• Six

• Twelve

If each outcome is equally likely, what is the probability of picking any one specific outcome?

• 1/9

• 1/12

• 1/6

• 1/3

Which of the following is NOT a possible outcome in the sample space?

• One day island trip

• Four day island trip

• Three day camping trip

• Two day ski trip

How many outcomes in the sample space involve a ski trip?

• Five

• Two

• Three

• Four

What is the probability of getting a vacation that lasts at least two days without snow?

• 5/9

• 2/9

• 3/9

• 4/9

Which of the following outcomes would satisfy the condition of at least two days without snow?

• One day camping trip

• One day island trip

• Two day ski trip

• Three day camping trip

If you want to avoid snow, which vacation type should you avoid?

• Island beach vacation

• Ski vacation

• Camping

• All of the above