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..
Hallie has a better chance of winning the grand prize by rolling two number cubes and hoping to get the same number on both cubes.
To calculate the probability of winning by spinning the wheel, we divide the number of sections with the desired outcome (getting a 5) by the total number of sections:
Probability of spinning a 5 = 1/6
To calculate the probability of winning by rolling two number cubes, we need to count how many possible outcomes in total there are and how many of them would result in the same number on both cubes.
There are 6 possible outcomes on each cube (numbers 1 through 6). The total number of possible outcomes when rolling two cubes is 6 x 6 = 36.
Out of these 36 outcomes, there are 6 outcomes where both cubes show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).
Probability of rolling the same number on both cubes = 6/36 = 1/6
Thus, the probability of winning the grand prize is the same in both cases (1/6). However, rolling two number cubes gives Hallie more chances to win because there are more possible outcomes. Therefore, her best bet is to roll two number cubes and hope to get the same number on both.
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Hallie has a better chance of winning the grand prize by rolling two number cubes and hoping for the same number on both cubes. The probability of winning by rolling two number cubes is 1/6 while the probability of winning by spinning a wheel and getting a 5 is also 1/6, but rolling two number cubes gives Hallie more chances to win. So she should roll two number cubes.
To determine which option Hallie should choose, we need to calculate the probabilities of each event.
First, let's consider spinning the wheel. The wheel has 6 equal sections labeled from 1 to 6. Since each section is equally likely to land on, the probability of getting a specific number, let's say 5, is 1 out of 6 or 1/6.
Now, let's analyze rolling two number cubes. Each cube has 6 sides, labeled with numbers 1 to 6. To calculate the probability of getting the same number on both cubes, we need to consider the total number of outcomes and the number of favorable outcomes.
The total number of outcomes when rolling two cubes is 6 x 6 = 36, as there are 6 possibilities for the first cube and 6 possibilities for the second cube.
The number of favorable outcomes, in this case, is 6. If Hallie rolls a 1 on the first cube, there is only one possibility (1) for the second cube to match. The same applies to rolling a 2, 3, 4, 5, or 6.
So, the probability of getting the same number on both cubes is 6 out of 36 or 6/36, which simplifies to 1 out of 6 or 1/6.
Comparing the probabilities, we can see that both options have the same probability of success. Therefore, it doesn't matter whether Hallie spins the wheel or rolls two number cubes. The chances of winning the grand prize are equal in both cases. Hallie can choose either option based on her preference.