At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to continue to spin the wheel until they win a prize. Define X = the number of spins a child takes until they win a prize.

Which, if any, of the following requirements for X to be a binomial random variable is violated in this setting?

a) The number of trials is fixed.

b) Each trial is independent of other trials.

c) There are two possible outcomes for each trial.

d) The probability of "success" is the same for each trial.

e) All requirements are met in this setting.

Question

Deacon

Mathematics

19 October, 09:41

At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to continue to spin the wheel until they win a prize. Define X = the number of spins a child takes until they win a prize.

Which, if any, of the following requirements for X to be a binomial random variable is violated in this setting?

a) The number of trials is fixed.

b) Each trial is independent of other trials.

c) There are two possible outcomes for each trial.

d) The probability of "success" is the same for each trial.

e) All requirements are met in this setting.

+3

Answers (1)

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Lorenzo Oconnor · Answer 1

(a) and (e) are not valid.

Step-by-step explanation:

a) The number of traials is not fixed. In fact, the random variable counts the total number of trials.

b) This is true, the result of each trial is independent of the others.

c) This is also true. The outcomes are failure and success.

d) This is true as well, all trials are identically distributed.

e) Since (a) is not valid, this cant be true.