Probability of Multiple Events

Question

There is a wheel of prizes at the county fair that costs 1 dollar to spin. Use this wheel of prizes to complete this activity.

1. Each black section takes up 1/4 of the wheel. If you land on that, you walk away with nothing.
2. The blue section takes up 1/8 of the wheel. If you land on that, you get a small prize (a piece of candy or bookmark).
3. The purple section takes up 1/8 of the wheel. If you land on that, you get a medium prize (a bracelet or a squirt gun).
4. The green section takes up 1/12 of the wheel. If you land on that, you get to spin again.
5. The red section takes up 1/12 of the wheel. If you land on that, you get a large prize (a stuffed animal or t-shirt).
6. The yellow section takes up 1/30 of the wheel. If you land on that, you get $5.
7. The orange section takes up 1/30 of the wheel. If you land on that, you get $10.
8. The white section takes up 1/60 of the wheel. If you land on that, you get the $50 jackpot.

1. If a player pays to spin the wheel twice, what is the probability that they will land on 0 at least once? Show your work and explain your process.

2. If a person spins the wheel twice, what is the probability of a jackpot for both spins? Show your work and explain your process.

3. What is the probability of a re-spin the first spin and winning money on the second spin? Show your work and explain your process.

4. What is the probability that a player will land on blue the first attempt and black the second attempt? Show your work and explain your process.

5. What is the probability that if a person spins twice, it will land on blue once and black once? Show your work and explain your process.

6. The answers to 4 and 5 should be different. What is the difference between these two questions? What are the vocabulary words we use to describe these two events? Use complete sentences

Answer 1

Hello Audrey J.,

If you have two successive events, you multiply the probability for the first event times the probability for the second event.

For example in the first one, getting two zeroes in a row really means landing on "no prize" twice in a row. "No prize" takes up 1/4 + 1/4 = 1/2 of the wheel.

P(no prize on both spins) = P(no prize on spin 1)P(no prize on spin 2) = (1/2)(1/2) = 1/4

See if you can work out the other ones.

Tom S.