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Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain
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Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain
To determine which option is better, we need to calculate the probability of each event occurring.
For spinning the wheel, there is only 1 way to get a 5 out of 6 possible outcomes. Therefore, the probability of getting a 5 is 1/6 or approximately 0.1667.
For rolling two number cubes, there are 6 possible outcomes on each cube (1, 2, 3, 4, 5, or 6). To get the same number on both cubes, there are 6 possible outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), or (6,6). Therefore, the probability of getting the same number on both cubes is 6/36 or 1/6, which is also approximately 0.1667.
Since the probabilities for both options are equal, it doesn't matter whether Hallie spins the wheel or rolls two number cubes. The odds of winning the grand prize are the same for either option. It may be more a matter of personal preference or superstition for Hallie to choose which method she wants to try.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain
To solve this problem, we need to compare the probabilities of winning the grand prize with each option.
For the wheel, there is only one way to get a 5 out of 6 possible outcomes. Therefore, the probability of winning with the wheel is 1/6 or approximately 0.1667.
For the number cubes, there are 6 possible outcomes on each cube (1, 2, 3, 4, 5, or 6). To win with the number cubes, both cubes must show the same number. There are 6 possible pairs of matching numbers, so the probability of winning with the number cubes is 6/36 or 1/6, which is also approximately 0.1667.
Since the probabilities of winning with each option are the same, it doesn't matter whether Hallie chooses the wheel or the number cubes. The odds of winning the grand prize are equal for both options. It may be more a matter of personal preference or superstition for Hallie to choose which option to try.
To determine which option Hallie should choose, let's analyze the probabilities of each event happening.
Option 1: Spinning the wheel and hoping for a 5
The wheel has 6 equal sections, so the probability of landing on any specific number (including 5) is 1 out of 6 or 1/6. Therefore, the probability of landing on a 5 is 1/6.
Option 2: Rolling two number cubes and hoping for the same number on both cubes
A standard number cube has 6 sides labeled from 1 to 6. When you roll one number cube, the probability of getting any specific number is 1/6.
To calculate the probability of getting the same number on both cubes, we need to consider that there are 6 possible outcomes for each roll of the first cube (1, 2, 3, 4, 5, or 6), and for each outcome, there is only 1 outcome on the second cube that will result in the same number.
Therefore, the probability of getting the same number on both cubes is 1/6 multiplied by 1/6, which simplifies to 1/36.
Comparing the probabilities of the two options, we have:
- Option 1: Probability of getting a 5 on the wheel = 1/6
- Option 2: Probability of getting the same number on both number cubes = 1/36
Since the probability of getting a 5 on the wheel is higher (1/6) than the probability of getting the same number on both cubes (1/36), Hallie should try her luck by spinning the wheel and hoping for a 5. The odds are more favorable in this case.