Question

A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes that 5 consecutive Is have occurred and bets heavily on black at the next spin. Asked why, he explains that "black is due."

Is the gambler's reasoning correct or incorrect? Justify your answer.

A) He is correct. If black and red are equally likely to occur, the wheel is due to land on black in order to even out the proportion of times it has landed on red.

He is incorrect. If 5 reds gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes that 5 consecutive Is have occurred and bets heavily on black at the next spin. Asked why, he explains that "black is due."
Is the gambler's reasoning correct or incorrect? Justify your answer.
He is correct. If black and red are equally likely to occur, the wheel is due to land on black in order to even out the proportion of times it has landed on red.
He is incorrect. If 5 reds occurred in a row, then reds are more likely to occur than black so he should always bet on red.
He is incorrect. The wheel is not affected by its past outcomes - it has no memory. So on any one spin, black and red remain equally likely.
He is incorrect. There is also green on the roulette wheel, which hasn't come up in the last 5 spins, so green is due as well.

B) He is correct. Because 5 reds occurred in a row there will be a streak of 5 blacks in a row next to balance out the outcomes occurred in a row, then reds are more likely to occur than black so he should always bet on red.

C) He is incorrect. The wheel is not affected by its past outcomes - it has no memory. So on any one spin, black and red remain equally likely.

D) He is incorrect. There is also green on the roulette wheel, which hasn't come up in the last 5 spins, so green is due as well.

E) He is correct. Because 5 reds occurred in a row there will be a streak of 5 blacks in a row next to balance out the outcomes

Answer 1

C

Explanation:

C) He is incorrect. The wheel is not affected by its past outcomes - it has no memory. So on any one spin, black and red remain equally likely.

The gambler's reasoning is based on a common misconception called the gambler's fallacy. The fallacy assumes that if an event has not occurred for a while, it is "due" to happen soon. However, in the case of a roulette wheel, each spin is an independent event, meaning the outcome of one spin has no impact on the outcome of the next spin.

Even though 5 reds have occurred in a row, the probability of black occurring on the next spin is still 18/38, which is the same probability as red. The wheel does not have any memory of past outcomes, so it does not need to "even out" the proportion of reds and blacks. Each spin is completely random and independent of previous spins unless it is rigged.