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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 compare the two options, we need to find the probability of winning with each method.
Method 1: Spinning the wheel
There is only one section with a 5 out of six total sections. Therefore, the probability of winning by spinning the wheel is 1/6.
Method 2: Rolling two number cubes
Each cube has six sides labeled with numbers 1-6. The probability of rolling any particular number on one cube is 1/6. We want to find the probability of rolling the same number on both cubes. We can do this by multiplying the probabilities of rolling the desired number on each cube.
Probability of rolling the same number on two cubes = (1/6) x (1/6) = 1/36
Comparing the probabilities, we see that the probability of winning with method 2 (rolling two number cubes) is much lower than the probability of winning with method 1 (spinning the wheel). Therefore, Hallie should try her luck by spinning the wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5.
To determine which option is more favorable for Hallie, we need to compare the probabilities of getting a 5 on the wheel spin and getting the same number on both number cubes.
Option 1: Spinning the wheel
The wheel has 6 equal sections, so the probability of getting a 5 is 1/6.
Option 2: Rolling two number cubes
Each number cube has 6 faces labeled from 1 to 6. To get the same number on both cubes, the first cube can land on any number from 1 to 6, and the second cube must then land on the same number.
The probability of the first cube landing on any particular number is 1/6. For the second cube to match, there's only one face that corresponds to the number rolled on the first cube. So, the probability of getting the same number on both cubes is 1/6 x 1/6 = 1/36.
Comparing the two probabilities:
The probability of getting a 5 on the wheel spin is 1/6, while the probability of getting the same number on both number cubes is 1/36.
Since 1/36 is smaller than 1/6, the probability of getting a 5 on the wheel spin is higher than getting the same number on both cubes.
Therefore, Hallie should try her luck by spinning the wheel and hope for a 5, as it has a higher probability of winning the grand prize than rolling the number cubes.