Chapter 12, Problem AP4.12CPT

To determine

To find out the random variable X has which of the following probability distribution.

Answer to Problem AP4.12CPT

Option (d) is the correct option.

Explanation of Solution

It is given that there are $\text{10 cards, 5 red and 5 black}\text{.}$ Also, it is given that the cards are shuffled and $1$ is randomly selected. The probability of red is $0.5$ and the probability of black is also $0.5$ (since $\text{5 out of the 10}$ cards are red and black). The key piece is that the card is replaced and once again shuffled; this ensures the next draw is independent of the first draw. This is repeated four times with the same exact probability of getting red and black.If X is the number of red cards, this would then be a binomial experiment. Thus, option (d) is the correct option.