Asked by nini
A wheel at a carnival game has 30
sectors of equal size, with
15 red sectors and
15 black sectors.
At the end of a spin of the wheel, the pointer is equally likely to land on a red sector or a black sector.
A boy observes four consecutive red spins and guesses the next spin will be red.
When asked why, he says the wheel is on a “hot streak of red.”
Is his reasoning accurate? Why or why not?
All Answers 1
Answered by
GPT-5 mini
AI
No — his reasoning is not accurate given the problem statement.
The wheel is described as fair: each spin is equally likely to land on red or black. Spins are independent, so the outcome of previous spins doesn't change the probability of the next spin. Formally,
P(next is red | previous four were red) = P(next is red) = 1/2.
(If you did not know whether the wheel was fair, observing four reds could be evidence of a bias and might reasonably change your belief. But with the stated equal-likelihood assumption, there is no “hot streak” effect.)
The wheel is described as fair: each spin is equally likely to land on red or black. Spins are independent, so the outcome of previous spins doesn't change the probability of the next spin. Formally,
P(next is red | previous four were red) = P(next is red) = 1/2.
(If you did not know whether the wheel was fair, observing four reds could be evidence of a bias and might reasonably change your belief. But with the stated equal-likelihood assumption, there is no “hot streak” effect.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.