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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.

Respuesta :

The following requirements for X to be a binomial random variable which are violated in this setting-

Option (a): The number of trials is fixed.

Option (e): All requirements are met in this setting.

Here, a player will spin the wheel until he/she wins a prize.

'X' denotes the number of spins a child takes until they win a prize.

Now, discussing the given options one by one-

Option (a): It's not valid as has been mentioned in the question that the game operator allows them to continue to spin the wheel until they win a prize.

Option (b): It is valid as each trial is not dependent on any other trial.

Option (c): It is valid as there are only two possible outcomes on spinning the wheel i.e., WIN or LOOSE.

Option (d): It is valid as there are only two possible outcomes on spinning the wheel so, the probability of WIN and LOOSE both are [tex]\dfrac{1}{2}[/tex].

Option (e): It is not valid as Option (a) is not meeting the requirement.

So, Option (a) and Option (e) are not violating the binomial random setting.

Learn more about binomial random variables here:

https://brainly.com/question/14282621?referrer=searchResults

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