Which of these random variables is most likely to have a binomial model?
A) The number of people we check until we find someone with green eyes.
B) The number of aces among the top 10 cards in a well-shuffled deck.
C) The number of Democrats among a group of 20 randomly chosen adults.
D) The number of cards of each suit in a 10-card hand.
E) The number of cars inspected until we find three with bad mufflers.

Question

Quizplus · Accepted Answer

A binomial model is appropriate when there are only two possible outcomes (success/failure), each trial is independent, the probability of success remains the same for all trials, and the number of trials is fixed. In option C, the possible outcomes are Democrat or not Democrat, the selection of each person is independent, the probability remains constant (assuming a random selection), and the number of trials is fixed at 20. Therefore, the number of Democrats among a group of 20 randomly chosen adults is the most likely to have a binomial model.

Which of These Random Variables Is Most Likely to Have