Probability Review

Probability Review General Probability

1. There are 8 red, 6 yellow, 4 green and 2 blue marbles in a bag. a. What is the probability of choosing a yellow marble? b. Calculate P(Yellow). c. Calculate P(Red or Yellow). d. What is the probability of choosing a green marble and then a blue marble if you replace the first one? e. What is the probability of choosing three yellow marbles in a row without replacement? f. What is the probability of choosing a red and a blue, in any order, with replacement?

2. What is the probability of rolling 4 fives in a row on a die?

3. Using a deck of cards as an example: a. Describe a probability event that is independent and explain why it is independent. b. Describe a probability event that is dependent and explain why it is dependent. c. Describe a probability event that is mutually exclusive and explain why it is mutually exclusive. d. Describe a probability event that is not mutually exclusive and explain why it is not mutually exclusive.

4. There are 10 red, 6 yellow, 5 green and 9 orange gumballs in a bag. If you get to eat the gum after making a choice, find the probability that the first 3 gumballs chosen will be green.

5. A standard deck of playing cards has 52 cards. It has 4 suits (red hearts, red diamonds, black spades and black clubs). Each suit has cards Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. If you select one card: a. Calculate P(2 or 4) b. Calculate P(Jack) c. Calculate P(5 or red)

6. You are planning a movie and game night. You need to choose between 4 movies, 3 different games, 5 types of treats and 2 nights to host the party. How many ways can you plan the evening?

7. You are at a restaurant and you have to choose between 2 appetizers (soup and salad), 2 meals (turkey and ham), and 2 desserts (pie and cake). a. Draw a tree diagram to represent this situation. b. Use the fundamental counting principle to determine the total number of meal options.

8. Determine whether the following events are dependent or independent. Justify your answers. a. Flipping a coin 5 times b. Getting a Jack and then a King from a deck of cards if you don’t replace the first card. c. Throwing 3 strikes in a row in a baseball game.

9. Postal codes in New Brunswick are in the form of letter number letter number letter number. How many different postal codes are possible?

Venn Diagrams

10. 50 students were asked which practical art they would choose for grade 12. The results are in the following diagram. Calculate: a. P(music) b. P(music and art) c. P(art only) d. P(music or art) e. P(art) Conditional Probability

11. A researcher was conducting a study of the link between eating fast food regularly and having major health problems. The researcher collected the data in the table below. Suppose that event A is “had major health problems” and event B is “ate fast food regularly”. Had major health Did not have major problems health problems Total Ate fast food 45 15 60 regularly Did not eat fast 20 20 40 food regularly Total 65 35 100

a. Calculate P(A and B). b. Calculate P(AB) c. Calculate P(BA) d. Calculate P(A) e. Compare P(A) to P(AB). What conclusion can this researcher make?

Permutations and Combinations

12. In your own words, describe the difference between permutations and combinations. In your explanation, include an example.

13. Evaluate the following expressions: 14. Write each of the following as a ratio of factorials.

a) 10! a) 12 x 11 x 10 x 9 x 8 x 7 b) 6! b) 23 x 22 x 21 x 20 c) 0! c) 6 x 5 x 4

15. In a poker tournament cash prizes are awarded to the top 10 people in the tournament. If 60 people enter the tournament, how many ways can the top 10 entrants finish (first, second, third, etc…)?

16. You win a draw at a charity event that allows you to randomly pick 3 music CD’s from a basket of 8. What is the probability that you will select your 3 favorite music CD’s the first favourite cd 1st, the second favourite, and third favourite CD 3rd?

17. Mrs. Parlee needs to select 4 students out of a class of 26 to do pick up some stuff from the office. How many ways can the 4 students be picked?

18. How many different arrangements are there for placing 8 textbooks on a shelf from left to right?

19. How many different combinations of 6 numbers can you make in Lotto 6/49 if you choose 6 numbers between 1 and 49 with no repetitions, and the order of the numbers doesn't matter?