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 whether Hallie should spin the wheel or roll the number cubes, we need to calculate the probabilities of each option.
1. Spinning the wheel:
The wheel has 6 equal sections labeled from 1 to 6. Since there is only one section labeled 5, the probability of landing on a 5 is 1 out of 6, or 1/6.
2. Rolling two number cubes:
A number cube, also known as a six-sided die, has numbers from 1 to 6. Hallie needs to roll two number cubes and hope to get the same number on both of them. To calculate the probability of this event, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes are rolls where both cubes show the same number. There are 6 possible outcomes, each representing one of the numbers on the first cube. For each of these outcomes, we have a 1 out of 6 chance that the second cube will also show the same number.
Thus, the probability of rolling two number cubes and getting the same number on both is (1/6) * (1/6) = 1/36.
Comparing the probabilities:
The probability of spinning a 5 on the wheel is 1/6, while the probability of rolling two number cubes and getting the same number on both is 1/36. Since 1/6 is greater than 1/36, Hallie has a higher probability of winning the grand prize if she spins the wheel rather than rolling the number cubes.
Therefore, Hallie should try her luck by spinning the wheel in the hope of getting a 5.