Your friend, Jamie, rolled a number cube and got the number 5. On his next turn, he says he won’t be able to roll another 5 because he is only expected to roll a 5 once every six rolls. Is your friend correct? Explain your answer.

Answer 1

Jamie is misunderstanding the nature of probability in this situation. Each roll of a number cube (a fair six-sided die) is independent of previous rolls. This means that the outcome of one roll does not affect the outcome of another roll.

The probability of rolling a 5 on a fair six-sided die remains constant at \( \frac{1}{6} \) for every single roll, regardless of past outcomes. Therefore, even though Jamie has rolled a 5 on his first turn, the next time he rolls the die, he still has a \( \frac{1}{6} \) chance of rolling another 5 on that roll.

In summary, Jamie's assertion that he won’t be able to roll another 5 on his next turn is incorrect. He still has the same probability of rolling a 5 again, which is \( \frac{1}{6} \).