Algebra 2 Probability & Combinatorics Worksheet 2 Problems 1-5: A bucket contains thirty balls, one for each integer from 1 to 30. 1. If one ball is randomly selected from the bucket, what is the probability of selecting a multiple of 7? Express your answer as a simplified fraction. 2. If one ball is randomly selected from the bucket, what are the odds against selecting a double-digit number? 3. If one ball is randomly selected from the bucket, what is the probability of selecting an even number or a multiple of 5? 4. If two balls are randomly selected from the bucket without replacement, what is the probability they will both be prime? 5. For a lottery, four different balls will be randomly selected from the bucket. How many different lottery tickets are possible? 6. A state issues vehicle license plates beginning with a number from 1 to 67 (indicating the county of issuance) followed by five characters which can be letters or digits. The letters I and O are not used, to avoid confusion with the numbers 1 and 0. How many different plates are possible? 7. How many permutations can be formed using all the letters in the word GIGGLING? 8. How many five-letter permutations can be made using the letters in the word CAMPGROUND? 9. A computer password is required to be exactly eight characters long, and the characters can be digits or letters. How many case-sensitive passwords are possible? How many noncase-sensitive passwords are possible? 10. A six-card hand is dealt from a standard deck. How many such hands contain four number cards and two non-number cards? [A number card is a card which has a number on it, not a letter.] 11. In how many different ways can three dice land? 12. What is the probability that the sum of three dice is less than 17? 13. If a point is randomly selected from the figure shown, what is the probability it lies in the shaded region? Round off your answer to the nearest tenth of a percent. Problems 14-15: The results of a survey are shown in the table. 14. What percent of the respondents own both a dog and a cat? 15. What percent of cat-owning respondents also own a dog? QUESTION Do you own a dog or a cat? Do you own a dog? Do you own a cat? Problems 16-20: A bucket contains 10 brown blocks, 8 purple blocks, and 12 orange blocks. 16. If one block is randomly selected from the bucket, what are the odds in favor of selecting an orange block? 17. If one block is randomly selected from the bucket, what is the probability of selecting a purple block? 18. If two blocks are randomly selected without replacement, what is the probability of selecting two brown blocks? 19. How many distinct permutations can be formed using five blocks from the bucket? 20. How many distinct permutations can be formed using all of the blocks from the bucket? CHALLENGE Refer to #16-19. If two blocks are randomly selected from the bucket, what is the probability that they will both be the same color? YES 82% 65% 49%