Hallie is trying to win the grand prize on a game show. Should she try her luck by doing a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll with two number cubes and hope she gets the same number on both cubes? Explain.
Hallie should roll with two number cubes, as the probability of getting the same number on both cubes is higher than the probability of getting a 5 on the wheel.
On the wheel, there is only one section that will result in a win for Hallie (the section labeled with a 5), out of a total of six sections. Thus, the probability of winning on the wheel is 1/6, or approximately 17%.
On the other hand, when rolling two number cubes, there are six possible outcomes where the two numbers are the same (1 and 1, 2 and 2, 3 and 3, etc.), out of a total of 36 possible outcomes (since there are six possible outcomes on one cube and six possible outcomes on the other). This gives a probability of winning of 6/36, or simplified, 1/6 (the same as the wheel). However, the advantage of rolling with two number cubes is that she has more chances to roll the same number than she has chances to land on the 5 in the wheel.
Therefore, rolling two number cubes is the better option for Hallie to increase her probability of winning the grand prize.