Unit 7 Probability Practice Test Name ____________________________________________________ Date_____________________Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. Show how you found the answer.

1. You want to select 4 candies from 15 candies that are displayed in the candy counter at a restaurant

Combination (15c4=13652. Rocky River is planning its RavenFest. All clubs will send 3 representative to help in the planning. How

many different groups of students can be chosen from 22 different clubs?Combination 22c3 =1540

3. For the women’s 100m dash in the Olympics, how many arrangements can be made for the gold medal, silver medal, and bronze medal finishers in a race with 40 athletes?

Permuation( 40p3 = 59280)4. The drama department is having auditions the upcoming play. How many ways can the top three leading

positions be filled if there are 21 at auditions?Permuation (21p3 = 7980Determine whether the events are independent or dependent. Then find each probability. Show work.

5. What is the probability of drawing three cards showing hearts from a standard deck of cards if the first card is not replaced before the next one is chosen?

Dependent (13/52)(12/51)(11/50) = 11/850

6. A bag contains 12 blue candy canes, 10 green candy canes and 15 red candy canes. If a candy cane is removed, replaced, and a second candy cane is picked, what is the probability that a green candy cane and then a red candy cane will be picked?

Independent (10/37)(15/37) = 150/1369

7. You have a CD with 15 rock songs, 11 blues songs, and 8 rap songs. Today you hit the shuffle button on your CD player which plays the songs in a random order. Tomorrow you do the same thing. What is the probability that the CD player plays a blues song first each day?

Independent (11/34)(11/34) = 121/1156

8. In a new board game that recently came out, a player can automatically win the game if they flip a head two times in a row. What is the probability of this happening?

Dependent (1/2)(1/2) = 1/4

Determine whether the events are mutually exclusive or inclusive. Then find the probability. Show work.

9. The letters of the alphabet are placed in a bag. What is the probability of selecting a P or one of the letters from the word GRADUATE?Mutually exclusive (1/26)+(8/26) = 9/26

10. The Math Club is selling pies to raise money. Bob’s prize for being the top seller of pies is a choice of a pie, a cupcake, or a bag of cookies. He can choose from 5 pies, 12 cupcakes, and 6 bags of cookies. What is the probability that Bob selects a pie or a cupcake?

Mutually exclusive (5/23)+(12/23)= 17/2311. If you pull a card from a standard 52-card deck, what is the probability that it is a black card or less than 3?

(Ace has a value of one)Overlapping (26/52)+(8/52) – (4/52) = 30/52 = 15/26

12. If you roll 2 standard 6-sided die, what is the probability of rolling a sum less than or equal to 9? Mutually exculusive 6/6 + 0/6 = certain will always happen.

Unit 7 Probability Practice Test Name ____________________________________________________ Date_____________________

For #13-15, P(A) = 0.45 and P(B) = 0.52. Assume that events A and B are mutually exclusive. Show work.Find the following:

13.P ( A∪B )

14.P( A ∩ B)

15. If events A and B were NOT mutually exclusive, find P ( A∪B )

A utility company asked 50 customers whether they pay their bills online or by mail. Show work.

16. What is the probability that she pays her bill online?36/50 = 18/25

17. Find P(female pay online)?

24/36 = 2/3

18. Find P( pay online female)?

24/30 = 4/5

19. The probability of getting a car for graduation is 0.38. What is the complement of this probability? Complement 1- .38 = .62 = 62%

The UNCC alumni association compiled the following information about its recent graduates.Use the data below to answer #20-22.

• 25% graduated with a B average or better• 85% of those students who graduated with a B average or better were employed within 6

months of graduation• 40% of those that graduated with less than a B average were employed within 6 months of

graduation

Did in class

20. Draw a tree diagram to show all probabilities.

21.What is the probability that someone is employed within 6 months of graduation, given that she had a C average?

22.What is the probability that someone is not employed within 6 months of graduation, given that he had an A average?

23.What is the probability that someone has an A average

Unit 7 Probability Practice Test Name ____________________________________________________ Date_____________________

given they have a job within 6 months of graduation?