In a carnival game, there are 8 identical boxes, one of which contains a prize. Contestants guess which box contains the prize. The game is played until one of the contestants guesses it correctly. A contestant with the smaller number of guesses wins the prize. Before each game, a new prize is placed at random in one of the 8 boxes.

Requried:
Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times?

Question

21-06-2021
Mathematics

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In a carnival game, there are 8 identical boxes, one of which contains a prize. Contestants guess which box contains the prize. The game is played until one of the contestants guesses it correctly. A contestant with the smaller number of guesses wins the prize. Before each game, a new prize is placed at random in one of the 8 boxes.

Requried:
Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times?

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joaobezerra joaobezerra · Answer 1 · 2022-02-21T12:00:59+01:00

Since there is a fixed number of trials and the trials are independent, it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

The game is played n times.

In each game, each of the 8 participants is equally as likely to win the game, hence p = 1/8.

Thus, the binomial distribution is appropriate.

You can learn more about the binomial distribution at https://brainly.com/question/24863377