A board game uses a deck of cards that players draw from to move tokens around the board. The probability of selecting a card that moves a player's token forward is 32%. Over the course of a game, the deck is shuffled and reused as necessary. Approximately how many cards must be drawn from the deck before players' tokens move forward 50 times?

Question

03-06-2022
Mathematics

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A board game uses a deck of cards that players draw from to move tokens around the board. The probability of selecting a card that moves a player's token forward is 32%. Over the course of a game, the deck is shuffled and reused as necessary. Approximately how many cards must be drawn from the deck before players' tokens move forward 50 times?

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joaobezerra joaobezerra · Answer 1 · 2022-06-10T12:48:03+02:00

Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

In this problem, the parameters are given as follows:

q = 50, p = 0.32.

Hence:

[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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