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Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".
a. Not binomial: there are more than two outcomes for each trial.
b. Procedure results in a binomial distribution.
c. Not binomial: the trials are not independent.
d. Not binomial: there are too many trials.

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Answer:

Correct option is b. Procedure results in a binomial distribution.

Step-by-step explanation:

Consider that X is Binomial random variable. The properties that are satisfied by X are:

  • There are n independent trials.
  • Each trial has only two outcomes: Success & Failure.
  • Each trial has the same probability of success.

Suppose a roulette wheel is spun and the number of times the ball lands on '16' is observed.

If the random variable X is defined as the number of times the ball lands on '16', then the random variable X follows a Binomial distribution.

Because,

  • Each spin is independent of each other
  • Success: The ball lands on '16'
  • Failure: The ball does not lands on '16'
  • The probability of the ball landing on '16' is [tex]\frac{1}{37}[/tex] for each trial.

Thus, the correct option is b. Procedure results in a binomial distribution.

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