Math Algebra Probability Key

Algebra 2 Honors Final Review Probability Name: Key Hour: 1. A briefcase lock has 3 rotating cylinders each containing 10 digits. How many numerical codes are possible? 10 * 10 * 10 = 1,000 2. Allan is playing the role of Oliver in his school's production of Oliver Twist. The wardrobe crew has presented Allan with 5 pairs of pants and 4 shirts that he can wear. How many possible costumes consisting of a pair of pants and a shirt does Allan have to choose from?   5 * 4 = 20 3. A Mexican restaurant offers chicken, beef, or vegetarian fajitas wrapped with either corn or flour tortillas, and topped with either mild, medium or hot salsa. How many different choices of fajitas does a customer have?   3 * 2 * 3 = 18 4. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, and no digit can be repeated? 8 * 9 * 8 * 7 * 6 * 5 * 4 = 483,840 5. How can 8 students be seated in 8 seats in the front row of the school auditorium? 8! = 40,320 6. How many ways can you check out 3 library books from a list of 8 books for a research paper? 8C3 = 56 7. How many ways can you elect 4 candidates to a municipal planning board from a field of 7 candidates? 7C4 = 35 8. How many ways can 10 contestants finish a race in first, second, and third place? 10P3 = 720 9. A student council has 5 seniors, 4 juniors, 3 sophomores and 2 freshmen as members. In how many ways can a 4-member council committee be formed that includes one member from each class?   5C₁ * 4C₁ * 3C₁ * 2C₁ = 5 * 4 * 3 * 2 = 120 10. How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no digit is used more than once?   5 * 4 * 3 = 60 11. Six representatives from a senior class of 350 students are to be chosen for the student council. In how many ways can these students be chosen to represent the senior class on the student council?   350C₆ Find the number of possible 5-card hands that contain the cards specified from a standard 52-card deck. 12. 4 kings and one other card 4C4 * 48C1 = 48 13. 5 hearts or 5 diamonds 13C5 + 13C5 = 2574 Find the number of distinguishable permutations in the following words. 14. PROBABILITY 11! / 2! = 9979200 15. PERMUTATION 9! / 2! = 181440 16. BEEKEEPER 9! / 2!2!1!1!1! = 30240 A letter is selected at random from those in the word TRIANGLE. Find the probability of each event. 17. It is a vowel. 3/8 18. It is from the upper half of the alphabet. 3/8 A card is randomly selected from a standard deck of 52 cards. Find the probability of drawing the given card. 19. A red king 2/52 = 1/26 20. A diamond or a 3 13/52 + 4/52 - 1/52 = 4/13 21. Not a club 39/52 = 3/4 Two cards are drawn at random from a 52-card deck. Find the probability of each event. 22. Both are hearts. 13/52 * 12/51 = 1/17 23. Both are jacks. 4/52 * 3/51 = 1/221 24. Neither is red. 26/52 * 25/51 = 25/102 25. Neither is a spade. 39/52 * 38/51 = 19/34 Two six-sided dice are rolled, one blue and one red. Find the probability of the given event. 26. The sum is 3 or 9. 6/36 = 1/6 27. The sum is greater than 7 and less than 11. 12/36 = 1/3 Find the odds in favor of an event, given the probability of the event. 28. 3/5 3:2 29. 1/3 1:2 30. 5/7 5:2 Find the probability of an event occurring, given the odds of the event. 31. 10:1 10/11 32. 4:9 4/13 33. 8:3 8/11 34. There are 3 nickels, 3 dimes and 5 quarters in a purse. Three coins are selected in succession at random. Find the probability   of: a. Drawing a nickel, then a dime, then a quarter if no replacement occurs 3/11 * 3/10 * 5/9 = 1/22 b. Drawing three quarters if replacement occurs 5/11 * 5/11 * 5/11 = 125/1331 c. Drawing a nickel and then two quarters if no replacement occurs 3/11 * 5/10 * 4/9 = 2/33 d. Drawing three quarters if no replacement occurs 5/11 * 4/10 * 3/9 = 2/33 35. Serena is creating a painting. She wants to use 2 more colors. She chooses randomly from 6 shades of red, 10 shades of green, 4 shades of yellow, 4 shades of purple and 6 shades of blue. What is the probability that she chooses 2 shades of green?   10C2 / 30C2 = 45/435 = 3/29 36. Becky's mother is shopping at the bakery. The owner offers Becky a cookie from a jar containing 22 chocolate chip cookies, 18 sugar cookies and 15 oatmeal cookies. Without looking, Becky selects one, drops it back in, and then randomly selects another. What is the probability that neither selection was   a chocolate chip cookie?   33/55 * 33/55 = 9/25