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

Answer 1

Answer:

d) The binomial distribution with n = 4 and p = 0.5

Step-by-step explanation:

They re 10 cards consisting of 5 red cards and 5 black cards which are shuffled thoroughly and choosing at random. After choosing the cards are replaced back.

The probability of choosing a red card = number of red cards / total number of cards = 5 / 10 = 0.5

The probability of choosing a black card = number of black cards / total number of cards = 5 / 10 = 0.5

Since after choosing, the cards are replaced back and shuffled making the next draw independent of the previous draw repeated four times. This is a binomial distribution with n = 4 and p = 0.5