Counting Methods and Probability Practice Set

  1. Directions

    Try answering these questions to practice what you have learned about counting methods and probability. Answers and explanations follow at the end of the chapter.

  2. Basic

    1. Paula has 10 books that she’d like to read on vacation, but she only has space for 3 books in her suitcase. How many different groups of 3 books can Paula pack?

    2. How many ways are there to fill a candelabra with 4 candle holders from a box of 6 distinctly colored candles?

    3. What is the probability of rolling a 6 on two consecutive rolls of a fair six-sided die?

    4. What is the probability that one roll of a fair six-sided die will result in an even number?

    5. Pablo is allowed to choose 1 of 3 different fruit beverages and 2 of 4 different healthy grain bars for his afternoon snack. How many different combinations does he have from which to choose?

  4. Intermediate

    1. A and B are overlapping sets. If |A| has 7 elements, |B| has 5 and  has 3 elements, how many elements are in ?

    2. What is the probability of the result of 4 independent coin flips being exactly 1 head and 3 tails?

    3. A bag contains only 4 orange marbles and 2 blue marbles. Latisha wants to get a blue marble from the bag, but she cannot see what color marble she draws until she takes it out of the bag. Latisha will stop drawing marbles as soon as she gets a blue one. If Latisha does not draw a blue marble in 3 attempts, she stops. What is the probability that she will draw a blue marble?

    4. Lee likes both country and pop music. Her playlist has a total of 60 songs that are categorized as pop, country, or rock. If a song is listed as both pop and country, it is considered crossover music. If 24 of Lee’s songs are classified as rock music only, 30 are pop, and 18 are country, how many are crossover? 

    5. A bag contains only red and blue plastic chips. There were 10 chips in the bag and 1 blue chip was removed. The probability of drawing a blue chip was then . How many red chips were in the bag?

  6. Advanced

    1. In a recent election for two different positions elected by the same voters, Candidates A and B were chosen by a majority of the voters. Two-thirds of the 60% of voters who chose candidate A also voted for Candidate B. The percentage of voters who did not vote for either candidate must have been less than ______?

    2. How many different-appearing arrangements can be created using all the letters AAABBC?

    3. A certain platoon is made up of 3 squads, each of which has 4 soldiers. When the platoon lines up to enter the mess hall, the squads are allowed to be in any order but the soldiers must line up within their squads according to certain rules. The soldiers in the first squad can line up any way they want as long as they stay with their squad. The squad leader of the second squad insists that the soldiers in that squad be in one particular order. The third squad leader wants the soldiers in that squad to line up in order from either tallest to shortest or shortest to tallest. How many different ways can the platoon line up?

    4. Events A and B are independent, but not mutually exclusive. The probability that event A occurs is 0.5 and the probability that at least one of the events A or B occurs is 0.8. What is the probability that event B occurs?

    5. A six-sided die used for a board game has the letter R on 3 sides, S on 2 sides, and T on the remaining side. What is the probability of rolling an R, an S, and a T on 3 rolls of the die, in any order?