Math Exam 1 study guide

Callie pays $5 to play the following game. She will spin the following spinner and win $25 if the spinner lands on diamond, win $10 if it lands on triangle, but nothing if it lands on square. Determine Callie's expected payback for playing the game one time.

$1.88

Events A and B are mutually exclusive. If P(A)=0.3 and P(B)=0.5 Find P(A∪B)

0.8

The odds that it will rain today are 2 to 9. What is the probability that it will rain?

2/11

The probability that a horse will win the race is 5/12. What are the odds against the horse winning?

7 to 5

Linda plays a game where she must draw a slip of paper from a bucket containing slips numbered 1 - 10. If she draws a 1 or 2, she wins $5. If she draws a 3, 4, or 5, she wins $1. Otherwise, she must pay $3. What is Linda's expected winnings for one drawing? Is the game fair? Why or why not?

E(X)= -$0.20 Not fair because E(X)≠0

The probability that a customer at Discount Tire Company needs to rotate his tires is 0.35. The probability that a customer will need a flat tire fixed is 0.15. The probability that a customer will need either his tires rotated or a flat tire fixed (or both) is 0.45. Determine the following: a) The probability that a customer needs to rotate his tires and needs a flat tire fixed b) The probability that a customer needs a flat tire fixed, given he needs to rotate his tires c) The probability that a customer needs to rotate his tires, knowing that he needs a flat tire fixed d) Are the events "a customer needs to rotate his tires" and "a customer needs a flat tire fixed" independent? Why or why not?

a) .05 or 1/20 b) 1/7 c) 1/3 d) No they are dependent because P(R)*P(F)≠P(R∩F)

The probability Venn diagram below reflects the results of a survey of people regarding the types of power tools they owned. a) What is the probability that a randomly chosen person does not own a drill or a saw? b) What is the probability that a randomly chosen person owns exactly one of the items? c) If a person that owns a saw was randomly selected, what is the probability that he also owns a drill?

a) .25 b) .56 c) 19/46

A game consists of picking one card from a deck of 52 playing cards. If a face card is drawn, the player wins $20. If an ace is drawn, the player wins $300. However, if any other card is selected the player must pay $40. a) What is the expected value of the game? b) Is the game fair? Why or why not?

a) 0 b) The game is fair because E(X)= 0

Let P(E)= 0.3, P(F|E)= 0.4, and P(F'|E')= 0.1 Find: a) P(F|E') b) P(E∩F) c) P(F')

a) 0.9 b) 0.12 c) 0.25

Two fair dice are rolled and the sum of the dice is recorded. Find the following probabilities. a) The sum is 9 or exactly one die shows a 5 b) The sum is at least 5

a) 1/3 b) 5/6

Draw two cards from a deck of 52 without replacement. Find the following probabilities: a) A spade second given that the first was a heart b) A club first c) A heart second d) Two hearts e) A spade first and a diamond second f) A spade and a diamond in any order

a) 13/51 b) 1/4 c) 1/4 d) 1/17 e) 13/204 f) 13/102

Two cards are drawn from a standard deck of 52 a) Find the probability that the second card is a heart given the first is a black card b) Find the probability that the second card is black given the first is a spade

a) 13/51 b) 25/51

A survey was conducted among a group of students to see how many questions they missed on their last history test. Below is a table of the results. a) What is the probability a student missed less than five questions? b) According to the data, what is the average number of questions missed on the test?

a) 29/84 b) 6.3452

In a council election, the percentage of males and females who voted for the two candidates are shown in the table. a) Find the probability that a randomly selected voter is male, given that the person voted for Stan b) Find the probability that a randomly selected voter did not vote for Gordon c) Find the probability that a randomly selected female voter voted for Stan

a) 31/53 b) .53 c) 11/20

A survey was taken of 200 college students. The survey asked if the students had eaten spaghetti, pizza, or hamburgers in the past month. Of the 200 students asked, 145 ate pizza 50 ate spaghetti 40 ate hamburgers but not pizza 115 ate pizza but not spaghetti 80 ate pizza and hamburgers but not spaghetti 20 ate all three foods 10 ate none of these foods a) How many students had eaten only pizza? b) How many students had eaten hamburgers and spaghetti, but not pizza?

a) 35 b) 15

A math class has 25 students, 10 of whom are engineering majors. 15 of the students are men, and of those 6 are engineering majors. a) Find the probability that a student is a female engineering major b) Find the probability that a student is a male given that he is an engineering major

a) 4/25 b) 3/5

A group of 100 students was surveyed, with the following results: 29 students read Sports Illustrated 36 students read ESPN The Magazine 70 students read the internet (espn.com, cnnsi.com, etc) 13 read Sports Illustrated and ESPN The Magazine 30 read ESPN The Magazine and the internet 19 read Sports Illustrated and the internet 10 read Sports Illustrated and the internet but not ESPN The Magazine a) How many students read only Sports Illustrated? b) How many people don't read any of the three items?

a) 6 b) 18

An experiment is to roll a 4-sided die and spin a spinner that is equally likely to land on green, red, or white. a) Determine the sample space for the experiment. b) Determine the following events: i. Spinner lands on red ii. Roll a 3 iii. Roll an odd number iv. Roll a three and land on green v. Roll an even number and do not land on white vi. Roll a three or land on red vii. Roll a multiple of 5 c) Determine the following probabilities: i. Spinner lands on red ii. Roll a 3 iii. Roll an odd number iv. Roll a three and land on green v. Roll a two or land on white vi. Land on yellow

a) S= {1g, 1r, 1w, 2g, 2r, 2w, 3g, 3r, 3w, 4g, 4r, 4w} b) i.) E= {1r, 2r, 3r, 4r} ii.) E= {3g, 3r, 3w} iii.) E= {1g, 1r, 1w, 3g, 3r, 3w} iv.) E= {3g} v.) E= {2g, 2r, 4g, 4r} vi.) E= {1r, 2r, 3g, 3r, 3w, 4r} vii.) E= { } c) i.) 1/3 ii.) 1/4 iii.) 1/2 iv.) 1/12 v.) 1/2 vi.) 0

Let C= {Adidas, Bass, Converse, Ecco, Nike, Puma, Reebok} True/False a) Nike ∈ b) {Adidas, Converse, Reebok} ∈ C c) {Bass, Ecco, Rockport} ⊆ C d) Ø ⊆ C

a) True b) False c) False d) True

Write the following sets as Venn Diagrams. a) A∩B b) A∪B c) A∩B' d) A∪(B∩C')

a) the middle part in between A and B. b) all regions, A, B, and middle but not the universe. c) Only region A not the middle or B. d) The whole region A including the ones that are intersecting with B and C. And there is only B at the top part.

The numbers 1 through 15 are written on balls and placed into a bucket, and one ball is drawn out of the bucket and recorded. a) What is the sample space for the experiment? b) Find the probability of the event F: a number less than 7 is drawn

a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} b) 2/5

Let A= {1, 2, 3, 4, 5}, B={1, 3, 5, 7, 9} C={x| x is an even natural number between 0 and 11} U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a) Find A∩B b) Find A∪B c) Find C' d) How many subsets does A have?

a) {1, 3, 5} b) {1, 2, 3, 4, 5, 7, 9} c) {1, 3, 5, 7, 9} d) 32

A die is rolled and then a coin is tossed. a) What is the sample space for the experiment? b) Find the probability that a three is rolled or heads is flipped

a) {1h, 1t, 2h, 2t, 3h, 3t, 4h, 4t, 5h, 5t, 6h, 6t} b) 7/12