Math 3201 Unit 3: Probability Name:

Transcription

1 Multiple Choice Math 3201 Unit 3: Probability Name: 1. Given the following probabilities, which event is most likely to occur? A. P(A) = 0.2 B. P(B) = C. P(C) = 0.3 D. P(D) = 2. Three events, A, B, and C, are all equally likely. If there are no other possible events, which of the following statements is true? A. P(A) = 0 B. P(B) = C. P(C) = 1 D. P(A) = 3 3. The odds in favour of Macy passing her driver s test on the first try are 7 : 4. Determine the odds against Macy passing her driver s test on the first try. A. 4 : 7 B. 4 : 11 C. 7 : 11 D. 3 : Julie draws a card at random from a standard deck of 52 playing cards. Determine the odds in favour of the card being a heart. A. 3 : 1 B. 1 : 3 C. 1 : 1 D. 3 : The odds in favour of Macy passing her driver s test on the first try are 7 : 4. Determine the probability that she will pass her driver s test. A B C D Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls out a coin at random. Determine the probability of the coin being a quarter. A B C D Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the wall 7 times in 28 attempts. Determine the probability of Zahra climbing to the top this time. A B C D

2 8. The weather forecaster says that there is an 80% probability of rain tomorrow. Determine the odds against rain. A. 4 : 5 B. 4 : 1 C. 1 : 5 D. 1 : 4 9. A sports forecaster says that there is a 75% probability of a team winning their next game. Determine the odds against that team winning their next game. A. 3 : 4 B. 1 : 3 C. 3 : 1 D. 1 : A credit card company randomly generates temporary three-digit pass codes for cardholders. The pass code will consist of three different even digits. Determine the total number of pass codes using three different even digits. A. 5 P 5 B. 5 P 3 C. 5 P 4 D. 5 P Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the number of options where at least one coin lands as heads. A. 1 B. 3 C. 5 D A credit card company randomly generates temporary four-digit pass codes for cardholders. Determine the number of four-digit pass codes. A. 10 B. 100 C D Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the total number of outcomes. A. 2 B. 4 C. 8 D Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the probability that only boys will be on the trip. A. 0.02% B. 0.08% C. 0.15% D. 0.23% 15. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the van. Determine the probability that only boys will be sitting at the front. A % B % C % D %

3 16. A and B are mutually exclusive events. P(A) = 55%. P(A B) = 80%. What is the P(B)? A. 15% B. 25% C. 45% D. 75% 17. Two dice are rolled. Let A represent rolling a sum greater than 10. Let B represent rolling a sum that is a multiple of 2. Determine n(a B). A. 1 B. 3 C. 11 D Select the events that are mutually exclusive. A. Drawing a 7 or drawing a heart from a standard deck of 52 playing cards. B. Rolling a sum of 4 or rolling an even number with a pair of four-sided dice, numbered 1 to 4. C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards. D. Rolling a sum of 8 or a sum of 11 with a pair of six-sided dice, numbered 1 to A and B are mutually Exclusive Events. If P(AUB) = 81% and the P(A) = 31%, what is the P(B)? A. 31% B. 50% C. 69% D. 112% Josie is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a red card or a 7. A. B. C. D.

4 22. Samuel rolls two regular six-sided dice. Determine the odds against him rolling an even sum or an 8. A. 1 : 3 B. 25 : 11 C. 21 : 15 D. 1 : Hilary draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine the probability that both cards are hearts. A. B. C. D. 24. Select the events that are dependent. A. Drawing a face card from a standard deck of 52 playing cards, putting it back, and then drawing another face card. B. Rolling a 4 and rolling a 3 with a pair of six-sided dice, numbered 1 to 6. C. Drawing a heart from a standard deck of 52 playing cards, putting it back, and then drawing another heart. D. Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered 1 to Select the events that are independent. A. Choosing a number between 1 and 30 with the number being a multiple of 2 and also a multiple of 4. B. Drawing a heart from a standard deck of 52 playing cards and then drawing another heart, without replacing the first card. C. Rolling a 2 and having a sum greater than 4 with a pair of six-sided dice, numbered 1 to 6. D. Rolling a 1 and rolling a 6 with a pair of six-sided dice, numbered 1 to Rino has six loonies, four toonies, and two quarters in his pocket. He needs two loonies for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are loonies. A. 16.3% B. 18.4% C. 22.7% D. 25.9% 27. Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the probability of drawing a five then drawing a two. A % B % C % D %

5 28. There are 20 cards, numbered 1 to 20, in a box. Two cards are drawn, one at a time, with replacement. Determine the probability of drawing an even number then drawing a number that is a multiple of 4. A. 8.8% B. 9.3% C. 10.7% D. 12.5% 29. Select the independent events. A. P(A) = 0.22, P(B) = 0.39, and P(A B) = B. P(A) = 0.18, P(B) = 0.7, and P(A B) = C. P(A) = 0.51, P(B) = 0.1, and P(A B) = D. P(A) = 0.9, P(B) = 0.23, and P(A B) = Select the independent events. A. P(A) = 0.21, P(B) = 0.57, and P(A B) = B. P(A) = 0.8, P(B) = 0.52, and P(A B) = C. P(A) = 0.74, P(B) = 0.85, and P(A B) = D. P(A) = 0.46, P(B) = 0.9, and P(A B) = Part II FCP, Permutations and Combinations 3-1 to A jar contains 6 red marbles and some green marbles. The odds against selecting a randomly chosen green marble are 1:4. Show all workings to determine how many green marbles are in the jar? 2 A 6 digit number is generated from the following digits 4, 2, 7, 9, 6, 5 with no repetition. Find the probability of the number that is formed that is will be: A) An odd number Total Outcomes:= B) An even number C) The odds against an even number being formed

6 3 There are 10 teachers and 4 administrators at a conference. A) Find the number of ways you can award 4 prizes to teachers only. (Remember order is not important) B) Find the number ways to give out the four prizes to all people at the conference? C) Find the probability that all of the 4 prizes went to teachers? To Administrators? 4 A jar contains 5 red, 8 blue and 10 purple candies. If the total number of candies is 30, find the probability that a handful of 4 contains one of each type? 5 Mark, Nancy, Olivia, Paul, Quinlan and Roxy are standing in a line. A) Determine the total possible arrangements. B) Determine how many ways Quinlan and Roxy could be standing together. Use this to determine the probability Quinlan and Roxy will be standing together? What are odds they will NOT be standing together? [3 questions here] C) What is the probability that Quinlan and Nancy are NOT standing together?

7 6 In a class survey, 54% play sports, 37% play a musical instrument, 24% play neither. A) Draw a Venn diagram to illustrate whether the events are mutually exclusive or non-mutually exclusive. Use it to determine B) the probability someone play a musical instrument or plays sports C) the probability someone does not play a musical instrument D) the probability someone plays a sport only 7 A person is being selected to draw a marble from a bag. The odds of selecting a male from the group are 7:10 while the odds of selecting a green marble are 1: 4. What is the PROABILITY of a non-green marble being selecting by a female in the group? (AND is implied YES or NO?)