Question

The expected probability of rolling an even number in 1 roll of a fair cube with faces numbered 1 through 6 is 1/2. When the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. When the same cube was rolled 100 times, an even number came up 51 times, or almost 1/2 the time.

Why are the actual results closer to the expected probability of 1/2 when rolling the cube 100 times?

a. A larger sample size was used.

b. The 100 tosses were controlled better.

c. The expected probability changed when the cube was rolled 100 times.

d. The thrower considered only the even rolls, and disregarded the odd rolls.

Answer 1

Explanation:

The correct answer is a. A larger sample size was used.As per the Law of Large Numbers, the more times an experiment is repeated, the closer the actual results will be to the expected probability. In this case, rolling the cube 100 times provides a larger sample size than rolling it only 20 times. The more rolls that are made, the greater the likelihood that the actual results will converge towards the expected probability of 1/2 for rolling an even number.Option b, The 100 tosses were controlled better, is not relevant to this scenario since the fairness of the cube is assumed.Option c, The expected probability changed when the cube was rolled 100 times, is not true. The expected probability of rolling an even number on a fair six-sided die is always 1/2, regardless of the number of times it is rolled.Option d, The thrower considered only the even rolls, and disregarded the odd rolls, is not a valid assumption. The question states that the number of even rolls was recorded, but it does not imply that odd rolls were disregarded.