Probability Review Questions Short Answer 1. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10 balls, numbered 1 to 10. 2. Teresa notices that bagels are on sale at a local grocery store. The last four times that bagels were on sale, they were available only once. Determine the odds in favour of bagels being available this time. 3. Elise rolls a standard die. Determine the odds against her rolling an even number. 4. A credit card company randomly generates temporary five-digit pass codes for cardholders. Meghan is expecting her credit card to arrive in the mail. Determine, to the nearest hundredth of a percent, the probability that her pass code will consist of five different even digits. 5. A computer manufacturer knows that, in a box of 175 computer chips, 5 will be defective. Max will draw 2 chips at random, from a box of 175. Determine, to the nearest thousandth, the probability that Max will draw 2 non-defective chips.
6. Ashley has letter tiles that spell NAPKIN. She has selected three of these tiles at random. Determine the probability that the tiles she selected are two consonants and one vowel. 7. Luke is playing a board game. He must roll doubles (event A) or a sum of 6 (event B). Draw a Venn diagram to represent the two events. 8. The probability that Randy will study on Friday night is 0.3. The probability that he will play video games on Friday night is 0.7. The probability that he will do at least one of these activities is 0.9. Determine the probability that he will do both activities. 9. Suppose that P(A) = 0.16, P(B) = 0.25, and P(A B) = 0.04. Are events A and B independent? Explain. 10. Brandon is playing a board game. He must roll two four-sided dice, numbered 1 to 4. Determine the probability that Brandon will roll a sum of 5 or a sum of 7.
11. Sonja has letter tiles that spell MICROWAVE. She has selected four of these tiles at random. Determine, to the nearest tenth of a percent, the probability that the tiles she selected are two consonants and two vowels. 12. Simone needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that her password will be greater than 3500. 13. Leanne rolls two six-sided dice, numbered 1 to 6. Determine the probability that she rolls a sum greater than 9 or a multiple of 4. 14. The probability that Vince will study on Friday night is 0.6. The probability that he will go out for dinner is 0.8. The probability that he will do at least one of these activities is 0.8. Determine the probability that he will do both activities. 15. A regular six-sided red die and a regular six-sided black die are rolled. The red die lands on 3 and the sum of the two dice is greater than 8. Are the two events dependent or independent? 16. Matias rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 2 and the sum of the two dice is greater than 4, Matias wins a point. Determine, to the nearest tenth of a percent, the probability that Matias will win a point. 17. Cheryl draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are black. 18. Janelle has eight identical black socks and two identical white socks loose in her drawer. She pulls out one sock at random and then another sock, without replacing the first sock. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of white socks. 19. Jasmine has two identical red marbles and twelve identical blue marbles in a paper bag. She pulls out one marble at random and then another marble, without replacing the first marble. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of blue marbles. 20. Access to a particular online game is password protected. Every player must create a password that consists of three capital letters followed by two digits. Repetitions are NOT allowed in a password. Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters J, K, and L. 21. A computer manufacturer knows that, in a box of 100 computer chips, 2 will be defective. Eric will draw 2 chips at random, from a box of 100. Determine, to the nearest thousandth, the probability that Eric will draw 2 non-defective chips. 22. A standard red die and a four-sided green die are rolled. Determine, to the nearest hundredth of a percent, the probability of rolling a 6 on the red die and a 2 on the green die. 23. Two cards are drawn without being replaced, from a standard deck of 52 playing cards. Determine, to the nearest hundredth of a percent, the probability of drawing an odd-numbered card (ace, 3, 5, 7, or 9) then a face card.
24. A die is rolled twice. Determine the probability that the first roll is greater than 3, and the second roll is less than 3. 25. A credit card company randomly generates temporary four-digit pass codes for cardholders. Serena is expecting her credit card to arrive in the mail. Determine the probability that her pass code will consist of four different odd digits. 26. State whether the following events are mutually exclusive and explain your reasoning. Drawing a heart or drawing a Jack from a standard deck of 52 playing cards.
Probability Review Answer Section SHORT ANSWER 1. Not mutually exclusive. e.g., 2 is both an even number and a prime number. 2. 1 : 3 3. 1 : 1 4. 0.12% 5. 0.944 6. 60% 7. 8. 0.1 9. Yes. P(A) P(B) = P(A B) 10. 37.5% 11. 47.6% 12. 65% 13. 14. 0.6 15. These two events are dependent. 16. 11.1% 17. 25% 18. 2.2% 19. 72.5% 20. 0.038% 21. 0.960 22. 4.17% 23. 9.05% 24. 25. 1.2% 26. Not mutually exclusive. e.g. A standard deck of 52 playing cards includes a Jack of hearts.