I just need the answers to these please I’ve been on it for a while and just want to move on

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 The odds of landing on the zero section is 1/2. The odds of not landing on it is also 1/2. Because we want to find the odds it will land at least once we can also find the odds that it won't land on zero and subtract that from 1.

The odds that it won't land is 1/2. The odds that will happen twice is 1/2 * 1/2 or 1/4. The odds that this won't happen is 1-1/4 or 3/4

2 The odds it will be a jackpot is 1/60. The odds this will happen twice in a row is 1/60 * 1/60 or 1/3600.

3 The probability of landing on the re-spin is 1/12. The odds of winning money is 1/30 + 1/30 + 1/60

this is 2/60+2/60+1/60 = 5/60 = 1/12. So the odds of re-spin then money is 1/12 * 1/12 or 1/144

4 Odds of blue is 1/8, odds of black is 1/2. The odds these would happen in that order is 1/8 * 1/2

1/16

5 The odds of blue is 1/8, black is 1/2. Since order doesn't matter this is an example of permutation.

The odds of it happening exactly blue first then black second is 1/16 but there are other ways for blue and black to happen in two spins. They are (Black Blue) and (Blue Black). Since there are two permutations of color the odds of blue and black happening in two spins (regardless of order is 2 *1/16 or 1/8.

6 Again the difference between the two is permutation and combination. Permutation doesn't care about order. Imagine a smoothie that has 3 fruit. It doesn't matter which order the fruit are placed into the smoothie. It always makes the same drink. This is a combination.

If you had a stacked ice cream then the order does matter. You can have vanilla then chocolate then strawberry or any permutation of the three. Sure it is the same ice cream, but they are different based on how you stack them.

The permutations of a number of items is the factorial of those items.

4 objects.

Permutation is 4! or 4 * 3 * 2 * 1 = 24.