Question

What is the expected distribution of outcomes when rolling a fair six-sided dice 100 times, and what would be the anticipated outcome if the dice were rolled 50,000 times instead?

A) The observed frequencies are due to chance, and with more rolls, the distribution will approach a more equal distribution among the six sides.
B) The observed frequencies indicate a biased dice, and with more rolls, the bias is likely to persist.
C) The observed frequencies suggest a pattern but would likely even out with more rolls due to the law of large numbers.
D) The observed frequencies are unexpected, and with more rolls, the distribution will remain similar due to inherent biases in the dice.

Answer 1

The expected distribution of outcomes when rolling a fair six-sided dice 100 times would be approximately 16-17 times for each side. With more rolls, such as in the case of rolling the dice 50,000 times, the observed frequencies would approach a more equal distribution among the six sides, as suggested by the law of large numbers.

Step-by-step explanation:

The expected distribution of outcomes when rolling a fair six-sided die 100 times follows the concept of theoretical probability. Since the die is fair, each side has an equal chance of landing face up. So, if you roll the die 100 times, you would expect each side to appear approximately 16-17 times. However, due to the inherent randomness of the process, the observed frequencies may not exactly match the expected distribution.

If the same fair die were rolled 50,000 times, the law of large numbers suggests that the observed frequencies would approach a more equal distribution among the six sides. This means that all six sides would appear roughly the same number of times.

Therefore, option C) The observed frequencies suggest a pattern but would likely even out with more rolls due to the law of large numbers is the correct answer.