Question

your friend, jamie, rolled a number cube and got the number 5. on his next turn, he says he wont 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.

Explanation:

When rolling a fair number cube (with numbers 1 - 6), each roll is an independent event. The probability of rolling a 5 on any single roll is $\frac{1}{6}$, meaning there's a 1 in 6 chance to roll a 5 every time, regardless of previous rolls. Just because he rolled a 5 once doesn't affect the probability of rolling a 5 on the next turn—he still has a $\frac{1}{6}$ chance to roll a 5 again. The "expected to roll a 5 once every six rolls" refers to the long - run average, not that he can't roll a 5 right after rolling one.

Answer:

No, Jamie is not correct.