Binomial Distribution — Test Answers

Each of the teams in a mixed volleyball league consists of 5 men and 5 women. There are 9 men and 10 women, including Julia, who are trying out for a team. How many possible teams would include Julia?

According to a poll, 56% of voters support funding a new community center. A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. If being in favor of the center is a success, what is the probability of a success for this binomial experiment?

A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades. How many 7-card hands are possible with 2 hearts, 2 diamonds, 2 clubs, and 1 spade? Assume that the order of the cards does not matter, and use the formula for combinations to find your answer.

Sonia rolls a six-sided number cube 12 times and records if she rolls a 2. What is the number of trials for this binomial experiment?

There are 12 teams, each representing a different country, in a women’s Olympic basketball tournament. In how many ways is it possible for the gold, silver, and bronze medals to be awarded? Use the formula for permutations to find your answer.

There are 4 seats available at a table in the lunch room of an elementary school, and 12 students are looking for seats. In how many ways can the seats at the table be filled with 4 of these 12 students?

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective. She decides to check several monitors and record if they are defective. Which of the following will make this process into a binomial experiment?

Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.

Dion flips a coin 20 times and records if it comes up heads. If getting heads is a success, what is the probability of a success on each flip?

A president and vice president will be selected from among 35 members of a board. Should permutations or combinations be used when determining the number of possible ways these offices can be filled?

A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?

Two percent of mobile phones produced at a factory are defective. Which of the following is a binomial experiment?

Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times?

Thirty-three percent of all students at a high school like beef stew. Out of 300 students, 40 are selected randomly and asked whether they liked beef stew. If liking beef stew is a success, what is the probability of a failure for this binomial experiment?

A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?

Janie flips a coin 70 times and records if it comes up heads. If getting heads is a success, what is the probability of a failure?

Of the 10 contestants in a televised quiz competition, 2 were eliminated during this week’s show, and 2 more will be eliminated during next week’s show. How many groups of 6 remaining contestants are possible a week from now? Assume that the show airs on the same day every week.

Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? Round the answer to the nearest thousandth.

Which statement is true?

How many permutations are possible for 11 objects taken 7 at a time?