Odds on the Wheel of Fortune
By: Nick & Olivia M.
When the Wheel of Fortune is spun there are 4 spaces that are 600$, 1 space that is 550$, 4 spaces that are 500$, two big bankrupt spaces and then two more very small bankrupt spaces that take up about a third of a normal sized space, 3 spaces for 650$, 1 space for a free play, 3 spaces for 700$, 1 lose a turn space, one 800$ space, one wild space, one 2500$ space, and one 900$ space.
An event that is possible on the Wheel of Fortune is spinning and landing on a bankrupt.
The probability of this event occurring is 8 / 72. The probability of event A tells you that you have a 2 2/3 out of 25 chance of landing on Bankrupt. There are four bankrupt spaces but two of them are smaller than the others and that is where the two thirds is from. The probability of not landing on a Bankrupt space is 64/72. There are very good odds that say you are not going to land on a bankrupt but it is still possible and does happen. There is a much higher chance of landing on a space that is not Bankruptcy than there is a chance of it landing on a space that is bankrupt.
Another event that is possible on The Wheel of Fortune is to land on a yellow space.
The probability of this happening is 1/12. This tells us that the chance of landing on a yellow space is not very high but there is still a chance. The probability of not landing on a yellow space is 11/12.There is a much higher chance of landing on a space that is not yellow, than there is a chance of actually landing on a yellow space
Independent means that the outcomes do not depend on each other. If the outcomes are dependent that means that one outcome relies on one another. Our two different events, landing on a yellow or landing on a bankrupt, are both independent of each other. If a yellow space is landed on, there is no effect on the chances of landing on a yellow space the next time, so that is a independent event. The probability of landing on a bankrupt and then landing on a yellow space next is P(A and B) = 8/72 x 1/12= 8/72 x 6/72= 7/648. We had to use the independent AND formula to figure out the probabilities of the combined outcomes. The value of this probability is showing that these are independent of each other and do not matter the outcomes.
If an event is mutually exclusive, this means that both of the events cannot both be true. Our events are mutually exclusive, we cannot land on both a bankrupt and a yellow space. I know that our events are mutually exclusive because there can only be one space to be landed on. P(A or B) of this probability is = 8/72 + 6/72 = 7/36. We had to use the formula that showed us what the probability was if we wanted to how much of a chance we had to land on the Bankruptcy OR the yellow space. This value shows us the probability of landing on one or the other and not both combined.If the events were not mutually exclusive, what is the significance of P(A and B)? If they are not mutually exclusive the significance of P(a and B) is showing what the chances are of landing on them both at the same time, which is impossible in our case.
The Multiplication Rule of Counting is if there are two ways of doing something, then there are a x b ways of performing both actions. This is used for finding the number of possible outcomes of an event.The Multiplication rule of counting could be used in a situation such as choosing an outfit for prom. You have to pick out a certain color shirt, certain color vest, certain color tie and so on, but there are only so many options.
Permutation is a way that a set or number of things can be arranged. Permutation and combination are not the same at all.The main difference between permutation and combination is that in a permutation the order matters but in a combination it does not matter. Permutation tells us how many possible different arrangements there are for a certain situation.Permutation can be calculated by using a calculator. If you plug 5! Into a calculator, then it will do 5x4x3x2x1 for you.An example of permutation could be how many different ways can we award first place, second place, and third place trophies out of a group of 15. 3 people can be awarded a trophy, and there are 15 people. After one person gets a trophy, there are only 14 left. Then another, so there are 13 left. This would look like 15x14x13.We do not need any after 13, so we can get rid of the permutation of 12. This would end up looking like (15!/15!-3!). This equals 2730. There are 2730 different ways to award three people trophies out of a group of 15.
Combination is the all different ways you can get certain outcomes. The difference between combination and permutation is that in combination the order of getting outcomes does not matter but in a permutation the order does matter. Combinations are used for figuring out how many different outcomes there can be when they do not have to be arranged in any certain way. Combinations can be calculated using a calculator or by hand, but calculator is easier. The formula is: n!/r!(n-r)! Or nCr. An example of combination could be how many different combinations of people, male and female, could be on a team. There are 7 boys and 3 girls. How many 4 person teams can be formed from the 10 people? If you do 10C4, there are 210 different combinations you could possibly have. But then you have to take into consideration how many boys and how many girl combinations you could have in each group.
An event that is possible on the Wheel of Fortune is spinning and landing on a bankrupt.
The probability of this event occurring is 8 / 72. The probability of event A tells you that you have a 2 2/3 out of 25 chance of landing on Bankrupt. There are four bankrupt spaces but two of them are smaller than the others and that is where the two thirds is from. The probability of not landing on a Bankrupt space is 64/72. There are very good odds that say you are not going to land on a bankrupt but it is still possible and does happen. There is a much higher chance of landing on a space that is not Bankruptcy than there is a chance of it landing on a space that is bankrupt.
Another event that is possible on The Wheel of Fortune is to land on a yellow space.
The probability of this happening is 1/12. This tells us that the chance of landing on a yellow space is not very high but there is still a chance. The probability of not landing on a yellow space is 11/12.There is a much higher chance of landing on a space that is not yellow, than there is a chance of actually landing on a yellow space
Independent means that the outcomes do not depend on each other. If the outcomes are dependent that means that one outcome relies on one another. Our two different events, landing on a yellow or landing on a bankrupt, are both independent of each other. If a yellow space is landed on, there is no effect on the chances of landing on a yellow space the next time, so that is a independent event. The probability of landing on a bankrupt and then landing on a yellow space next is P(A and B) = 8/72 x 1/12= 8/72 x 6/72= 7/648. We had to use the independent AND formula to figure out the probabilities of the combined outcomes. The value of this probability is showing that these are independent of each other and do not matter the outcomes.
If an event is mutually exclusive, this means that both of the events cannot both be true. Our events are mutually exclusive, we cannot land on both a bankrupt and a yellow space. I know that our events are mutually exclusive because there can only be one space to be landed on. P(A or B) of this probability is = 8/72 + 6/72 = 7/36. We had to use the formula that showed us what the probability was if we wanted to how much of a chance we had to land on the Bankruptcy OR the yellow space. This value shows us the probability of landing on one or the other and not both combined.If the events were not mutually exclusive, what is the significance of P(A and B)? If they are not mutually exclusive the significance of P(a and B) is showing what the chances are of landing on them both at the same time, which is impossible in our case.
The Multiplication Rule of Counting is if there are two ways of doing something, then there are a x b ways of performing both actions. This is used for finding the number of possible outcomes of an event.The Multiplication rule of counting could be used in a situation such as choosing an outfit for prom. You have to pick out a certain color shirt, certain color vest, certain color tie and so on, but there are only so many options.
Permutation is a way that a set or number of things can be arranged. Permutation and combination are not the same at all.The main difference between permutation and combination is that in a permutation the order matters but in a combination it does not matter. Permutation tells us how many possible different arrangements there are for a certain situation.Permutation can be calculated by using a calculator. If you plug 5! Into a calculator, then it will do 5x4x3x2x1 for you.An example of permutation could be how many different ways can we award first place, second place, and third place trophies out of a group of 15. 3 people can be awarded a trophy, and there are 15 people. After one person gets a trophy, there are only 14 left. Then another, so there are 13 left. This would look like 15x14x13.We do not need any after 13, so we can get rid of the permutation of 12. This would end up looking like (15!/15!-3!). This equals 2730. There are 2730 different ways to award three people trophies out of a group of 15.
Combination is the all different ways you can get certain outcomes. The difference between combination and permutation is that in combination the order of getting outcomes does not matter but in a permutation the order does matter. Combinations are used for figuring out how many different outcomes there can be when they do not have to be arranged in any certain way. Combinations can be calculated using a calculator or by hand, but calculator is easier. The formula is: n!/r!(n-r)! Or nCr. An example of combination could be how many different combinations of people, male and female, could be on a team. There are 7 boys and 3 girls. How many 4 person teams can be formed from the 10 people? If you do 10C4, there are 210 different combinations you could possibly have. But then you have to take into consideration how many boys and how many girl combinations you could have in each group.