Chapter 12, Problem 12PT4

To determine

To find: the one of the following probability distributions for the random variable X on the basis of given information.

Answer to Problem 12PT4

  $X~binomial\left(4,0.5\right)$

Explanation of Solution

Given:

10 cards, five red and five black.

  $X~binomial\left(4,0.5\right)$

The cards are changed and 1 is picked randomly. Red is 0.5 and black is also 0.5 (because 5 of the 10 cards are red and black). The main point is that the card is changed and shuffled again. This means that the next draw is independent from the first draw. The same chance of turning red and black is replicated four times. This would then be a binomial exercise if X was the number of red cards.

Hence, the correct option is (d)