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? .
Hallie should roll two number cubes and hope to get the same number on both cubes.
The probability of getting a 5 on the wheel is 1/6 or approximately 16.67%.
The probability of getting the same number on both number cubes is 1/6 (the probability of getting any specific number on one cube) multiplied by 1/6 (the probability of getting the same number on the second cube). This equals 1/36 or approximately 2.78%.
Therefore, Hallie has a higher probability of winning the grand prize by rolling two number cubes and hoping to get the same number on both cubes.
To determine the better option for Hallie, let's analyze the probabilities of winning in both scenarios:
1. Spinning the wheel with 6 equal sections labeled from 1 to 6:
- Since there are 6 sections on the wheel, the probability of landing on any specific number (such as 5 in this case) is 1/6 or approximately 0.1667.
- Therefore, the probability of winning by spinning the wheel and landing on a 5 is 0.1667 or 16.67%.
2. Rolling two number cubes and hoping to get the same number on both cubes:
- With two number cubes, each cube has 6 sides, numbered from 1 to 6.
- The probability of rolling a specific number on one cube is 1/6 or approximately 0.1667.
- The probability of getting the same number on both cubes is the product of the probability of rolling the same number on each cube, which is (1/6) * (1/6) = 1/36 or approximately 0.0278.
- Therefore, the probability of winning by rolling two number cubes and getting the same number is 1/36 or 2.78%.
Comparing the probabilities, we can see that spinning the wheel has a higher probability of winning (16.67%) compared to rolling two number cubes and getting the same number (2.78%).
Thus, Hallie should try her luck by spinning the wheel and hoping to get a 5.