I need the answers to these please

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

1. Let's start with the overall probability of hitting 0. Since the probability of black section is 1/4 each, then the overall probability of hitting 0 is 1/2. So if you spin twice, you could miss the black section on both, hit it on one spin, or hit it on both spins. To be efficient, let's calculate the chances of missing the black section on both and subtracting from 1 a.k.a inverse probability.
2. Pr( at least once) = 1-Pr(never hitting black section) = 1-.5^2 = 0.75
3. Pr(jackpot)*Pr(jackpot) = (1/60)*(1/60) = 1/3600
4. Pr(respin and winning money) = Pr(respin)*Pr(winning money)

Pr(winning money) = Pr(yellow)+Pr(orange)+Pr(white) = 1/30 +1/30 +1/60= 1/12

Pr(respin and winning money) = 1/12 *1/12 = 1/144

4.Pr(blue and black) = Pr(blue)*Pr(black) = 1/8*1/2 = 1/16. Since the spins are independent of one another.

5.Pr(blue once and black once) = 1/16*2 = 1/8.

6. Question 4 takes order into account, question 5 doesn't. So in Q5 you have to account for blue coming first or black coming first. Since the probability is the same, you just need to double it.

Answer 2

Hello,

So you stated each black section takes up 1/4 of the entire circle. There are two sections of black.

1/4+1/4 = 1/2. Therefore, there is a probability 1/2 that someone that spins the wheel receives no prize.

1. One wheels spin doesn't impact another's i.e if we spin the wheel once, then spin it a second time. The result of the first spin doesn't impact our result on the second. The problem also states at least once, meaning the we land in the black region on the first spin, second spin or both spins.

I hope this answer steers you into the proper direction!