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During a game of roulette, a wheel is spun and a ball drops randomly into one of the wheel's numbered compartments. Then the process is repeated with another random spin.\newlineAre these two events dependent or independent?\newlineChoices:\newline(A) dependent\newline(B) independent

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Identify independent and dependent eventsright chevron icon

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Q. During a game of roulette, a wheel is spun and a ball drops randomly into one of the wheel's numbered compartments. Then the process is repeated with another random spin.\newlineAre these two events dependent or independent?\newlineChoices:\newline(A) dependent\newline(B) independent
  1. Understand Nature of Events: The first step is to understand the nature of the events in question. In roulette, each spin of the wheel is an independent event because the outcome of one spin does not affect the outcome of the next spin. The wheel has no memory of previous spins, and each spin is random.
  2. Events Independence in Roulette: To further clarify, if events are independent, the probability of both events occurring is the product of the probabilities of each event occurring separately. In the case of roulette, the probability of the ball landing in any given compartment on one spin does not change the probability of where it will land on the next spin.
  3. Correct Choice Explanation: Since each spin of the roulette wheel is independent, the correct choice between the given options (A) dependent and (B) independent is (B)(B) independent.

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