Question

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.

Answer 1

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

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
  `(1)/(37)` for each trial.

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