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Statistics / The Practice of Statistics 5 / Chapter 12 / Problem AP4.12

The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor

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A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled

Chapter 12, Problem AP4.12

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QUESTION:

A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of four times. Let X be the number of red cards observed in these four trials. The random variable X has which of the following probability distributions? (a) The Normal distribution with mean 2 and standard deviation 1 (b) The binomial distribution with n = 10 and p = 0.5 (c) The binomial distribution with n = 5 and p = 0.5 (d) The binomial distribution with n = 4 and p = 0.5 (e) The geometric distribution with p = 0.5 AP4

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QUESTION:

A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of four times. Let X be the number of red cards observed in these four trials. The random variable X has which of the following probability distributions? (a) The Normal distribution with mean 2 and standard deviation 1 (b) The binomial distribution with n = 10 and p = 0.5 (c) The binomial distribution with n = 5 and p = 0.5 (d) The binomial distribution with n = 4 and p = 0.5 (e) The geometric distribution with p = 0.5 AP4

ANSWER:

Step 1 of 2

The random variable represents the number of red cards observed in four trials. Since the represents the number of successes in several numbers of trials, the random variable has a Binomial distribution. We denote

where;

- is the number of trials,

- is the probability of success.

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