Asked by t
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 information.
Because the wheel has 30 equal sectors (15 red, 15 black) and each spin is equally likely to land on any sector, spins are independent and P(red) = 15/30 = 1/2 on every spin. The probability the next spin is red, even after four reds in a row, remains 1/2. The boy is committing the “hot‑hand” fallacy — assuming a streak makes the next outcome more likely — whereas for independent trials past results don’t affect future ones.
(If you did not know the wheel was fair, observing four reds could reasonably change your belief about a possible bias. But the problem states the spins are equally likely, so no update is needed.)
Because the wheel has 30 equal sectors (15 red, 15 black) and each spin is equally likely to land on any sector, spins are independent and P(red) = 15/30 = 1/2 on every spin. The probability the next spin is red, even after four reds in a row, remains 1/2. The boy is committing the “hot‑hand” fallacy — assuming a streak makes the next outcome more likely — whereas for independent trials past results don’t affect future ones.
(If you did not know the wheel was fair, observing four reds could reasonably change your belief about a possible bias. But the problem states the spins are equally likely, so no update is needed.)
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