A game is played where the contestant is asked to reach into a well-shaken bag c

Question

A game is played where the contestant is asked to reach into a well-shaken bag containing an equal number of red, yellow, and green marbles. Each time he selects a marble, he notes its color and places the marble back in the bag. The bag is then shaken well, and he selects again. After 15 selections, the the total number of times each color was selected is recorded. The contestant is awarded points based on the number of times each color is selected after 15 selections.

iI need to know if all requirements are met for it to be considered a binomial experiment

Explanation / Answer

The conditions of binomial experiment are

1) There must be only 2 outcomes to the experiment

2) The probability of an outcome must remain the same throughout the experiment

3) The number of trials must be fixed

Here, number of trial is fixed as 15 and the process by which balls are drawn makes sure that the probability of drawing any ball will remian constant throughout.

But to we cannot comment if the experiment satisfies the first condition or not, because the experiment is not well defined. If the expermient is such that the number of green colours defines the number of point, then the only two outcomes are either 'green' or 'not green'. In this case, its a binomial distribution

But if the experiment says that the point varies for each colour, then there can be many probabilities as there are many outcomes possible. In such cases, its not a binomial distribution

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