chapter 3
A doctor gives a patient a 75% chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, then the patient has a 60% chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals. Formula: P(survives) = 0.75 P(heals&survives) = .6 0.6x0.75 = .45
.45
Identify the two events described in the study and determine if the results indicate that the events are independent or dependent. Explain your reasoning. A study found that there is no relationship between being around alcohol abuse and developing skin cancer. 1. identify the 2 events 2. independent or dependent
1. Being around alcohol abuse and developing skin cancer. 2. Independent. Being around alcohol abuse does not cause skin cancer.
A study found that people who suffer from obstructive sleep apnea are at increased risk of having heart disease. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? 1. identify the 2 events 2. independent or dependent?
1. sleep apnea and heart disease 2. dependent
Identify the sample space of the probability experiment. Draw a tree diagram. Determining a person's grade (freshman (F), sophmore (So), junior (J), senior (Se)) and gender (male (M), female (F)) 1. identify the sample space 2. number of outcomes 3 tree diagram
1. {FM, FF, SoM, SoF, JM, JF, SeM, SeF} 2. 8 outcomes 3. F So J Se M F M F M F M F
There are 49 runners in a race. How many ways can the runners finish first, second, and third? Formula: 49x48x47
110544
Of the cartons produced by a company, 4% have a puncture, 11% have a smashed corner, and 2.1% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. Formula: = 4%+11%−2.1% = 12.9%
12.9%
There are 12 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth? formula: 12x11x10x9x8
95040
A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 10 choices for an entrée, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert? Formula: 4x10x3
A meal can be chosen in 120 ways.
You are planning a three-day trip to Seattle, Washington, in October. Use the fact that on each day, it could either be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question. What is the probability that it is sunny all three days?
.125
You are planning a three-day trip to Seattle, Washington, in October. Use the fact that on each day, it could either be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question. What is the probability that it rains all three days?
.125
Assuming that no questions are left unanswered, in how many ways can a twelve-question true-false quiz be answered? Formula: 2x2x2x2x2x2x2x2x2x2x2x2 2 times itself 12 times
4096
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 20C4 Formula: 20!/(20-4)!4! n!/(n-r)!r!
4845
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)=P(A)+P(B)−P(A or B).
False, the probability that A or B will occur is P(A or B)=P(A)+P(B)−P(A and B).
Twenty-seven of the 100 digital video recorders(DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is notdefective?
The probability is .73
For the given pair of events, classify the two events as independent or dependent. Finding that your cell phone works Finding that your dvd player
The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
What is the difference between independent and dependent events?
Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.
(a) List an example of two events that are independent. (b) List an example of two events that are dependent.
a. Rolling a die twice b. Drawing one card from a standard deck, not replacing it, and then selecting another card
A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution on the right shows the results. Use the table to answer the following question. What is the probability that the next person surveyed is very prepared? Very prepared - 304 Somewhat prepared - 914 Not too prepared - 619 Not at all prepared - 366 Not sure - 92 Total: 2295 Formula: 304/2295 frequency of e/total f
.132
According to a study, 68% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 68%, 11 out of 25 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. Formula: P(A) = 68% = .68 11/25 = .44 .44x.68 = .299
.299
A physics class has 80 students. Of these, 28 students are physics majors and 31 students are female. Of the physics majors, 15 are female. Find the probability that a randomly selected student is female or a physics major. Formula: fem+phys-(fem&phys) 31/80+28/80-15/80 = .550
.550
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. You randomly select one card from a standard deck of 52 playing cards. Event A is selecting a red four. 1. how many outcomes 2. is it simple
1. 2 outcomes 2. no, bc there is more than 1 outcome
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a number from the even numbers between 1 and 10, inclusive 1. number of outcomes 2. sample space
1. 2, 4, 6, 8, 10 2. 5 outcomes
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 40P2 formula: 40!/(40-2)! n!/(n-r)!
1560
A class has 40 students. In how many different ways can seven students form a group for an activity? (Assume the order of the students is not important.) formula: 40C7 40!/(40-7)!7!
18643560
In order to conduct an experiment, 9 subjects are randomly selected from a group of 49 subjects. How many different groups of 9 subjects are possible? Formula: 49C9 49!/(49-9)!9!
2054455634
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of three digits. The first digit cannot be seven and the last digit must be odd. How many different codes are available? (Note that 0 is considered an even number.) Formula: 9x10x5 In this case, the number of events is equal to the number of digits in the lock box's access code. There are 3 events in this situation. There are 9 choices for the first digit, because it can be any number from zero to 9 except 7. There are 10 choices for the second digit, because it can be any number from zero to 9. There are 5 choices for the third digit because this digit must be odd, that is, it must be 1, 3, 5, 7, or 9.
450
Outside a home, there is a 7-key keypad with letters A, B, C, D, E, F, and G that can be used to open the garage if the correct seven-letter code is entered. Each key may be used only once. How many codes are possible? Formula: 7! or 7x6x5x4x3x2x1
5040
Determine whether the events are independent or dependent. Explain your reasoning. Returning a rented movie after the due date and receiving a late fee
The events are dependent because the outcome of returning a rented movie after the due date affects the probability of the outcome of receiving a late fee.
A random number generator is used to select an integer from 1 to 100 (inclusively). What is the probability of selecting the integer 582?
The probability is 0
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a heart and then selecting a club
The probability of selecting a heart and then selecting a club is .064
The probability that an event will happen is P(E)=28/41. Find the probability that the event will not happen.
The probability that the event will not happen is 13/41.
Determine whether the following problem involves a permutation or a combination and explain your answer. How many different 2-letter passwords can be formed from the letters L, M, N, O, P, Q, and R if no repetition of letters is allowed?
The problem involves a permutation because the order in which the letters are selected does matter.
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. A combination is an ordered arrangement of objects.
The statement is false. A true statement would be "A permutation is an ordered arrangement of objects."
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a heart or club. (b) Compute the probability of randomly selecting a heart or club or diamond. (c) Compute the probability of randomly selecting an eight or spade.
a. 0.5 b. 0.75 c. 0.308
The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year Business Nonbusiness Male 205638 661358 Female 155618 968603 Total 361256 1629961 Total Male: 866996 Total Female: 1124221 Total Overall: 1991217 (a) Find the probability that a randomly selected student is male, given that the student received a business degree. Formula: 205638/361256 number of outcomes in event E/total number of outcomes in sample space (b) Find the probability that a randomly selected student received a business degree, given that the student is female. Formula: 155618/1124221
a. 0.569 b. 0.138
The access code for a safe consists of three digits. Each digit can be any number from 0 through 8, and each digit can be repeated. (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?
a. 729 b. .001 c. .999