Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8 Name: 45 1. A customer chooses 5 or 6 tapes from a bin of 40. What is the expression that gives the total number of possibilities? 2. A group of 4 journalists is to be chosen to cover a murder trial. There are 5 male and 7 female journalists available. How many possible groups can be formed, consisting of 2 men and 2 women? 3. As a promotion, a music store placed 12 tapes in one basket and 10 compact discs in another basket. The 1000 th customer to come through the store was allowed to select four tapes and four CD s. How many different selections could be made?
4. A hockey team has had a rough start to the season. The goal is to finish the preseason with as many wins as losses. The team has 20 preseason games and so far has 4 win and 8 losses. In how many ways can the team play the last eight games to finish with as many wins as losses? 5. A door to door salesperson visited 140 homes in a working day. Sixty of the people showed no interest in the product. Of the remainder of people, 30 bought something and 10 of those 30 customers bought more than $500 in merchandise. a. What is the probability that a potential customer will show some interest? b. What is the probability that a potential customer will buy something? c. If a potential customer initially shows some interest, what is the probability that $500 in merchandise will be bought? 6. Carl spent 30 min in a batting cage. The pitching machine delivered 180 balls in that time. Carl hit 102 of them but 30 were foul. a. What is the probability that Carl will hit any given pitch? b. What is the probability that Carl will have a fair hit on any given pitch? c. If Carl hits the ball, what is the probability that it will be fair?
7. Suppose you took a census at your school and found the following frequencies of blood types. Blood Type A B AB O Frequency 78 22 8 92 If you chose five students at random, what would be the probability of each outcome? d. Finding five with type O e. Finding five with type B 8. A poll found that the probability that a student chosen at random had visited the arcade within the past week was 0.3. The probability that a student chosen at random played games on a home-based game machine was 0.5. The probability that a student did both was 0.2. What was the probability that a student played on an arcade machine or on a home-based machine? 9. One card is removed at random from a full deck. What is the probability of each event? a. Removing a spade b. Removing a face card or a heart 10. What is the probability of rolling a sum of 7 or 11 with one roll of two dice?
11. A census was taken of the students in a small rural high school. The students were asked if they were currently taking a course that used distance education technology. The results are summarized below. Yes No Female 8 14 Male 5 11 What is the probability that a male student in the school is taking a distance education course? 12. Four green marbles and six red marbles are in a bag. a. Find the probability of drawing a green marble and then a red marble, if the marbles are not replaced. b. Find the probability of drawing a green marble and then a red marble, if the marbles are replaced. 13. What is the probability of drawing a heart or a club from a deck of cards? 14. What is the probability of drawing a red card or a queen from a deck of cards?
15. In a school lottery, participants choose four numbers between 1 and 100. No number is repeated. What is the probability of guessing the winning numbers? 16. A line-up of seven suspects includes four criminals with outstanding arrest warrants. If the police randomly check for arrest records on four of the suspects, what is the probability of discovering the four wanted criminals? 17. Five cyclists line up for a race. What is the probability of correctly guessing the first-, second-, and third-place finishers in order? 18. A plumber is fixing a basin faucet and is reaching blindly in to a container for three compression fittings. The container holds four that will fit the pipe and two that are slightly too small. What is the probability that she will get three that will fit? 19. A class of 12 has 7 Maple Leaf fans and 5 Canadiens fans. Three tickets to a Leafs game are given away a random what is the probability that all the tickets will go to Leafs fans?
20. A scratch-and-win lottery ticket has 16 prize boxes. Under the boxes are four pictures of a videogame machine, five pictures of video-game software, and six pictures of movie tickets. Players scratch four boxes. If they scratch four identical pictures, they win the prize represented by the pictures. a. What is the probability of winning the video-game machine? b. What is the probability of winning any prize? 21. On Saturday, you went to Crazy Wally s Fair down the street. You play one of the games and win! Your prize is to pick two prizes out of a box. In the box are 20 chocolate bars, 2 mp3 players and 10 erasers. What is the probability of you getting an mp3 player and a chocolate bar? 22. A 13-card hand was dealt from a deck of 52 cards. What is the probability that a. there are no spades? b. there are 2 hearts, 3 diamonds, 5 spades and 3 clubs?