Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axi…
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between…
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Chapter 12.CR, Problem 76CR
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The probability of getting the sum of no more than 5 when two fair dice are rolled.

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f(x) = = x - 3 x²-9 f(x) = {x + 1 x > 3 4 x < 3 -10 5 10 5 5. 10 5- 07. 10 -10 -5 0 10 5 -101 :: The function has a “step" or "jump" discontinuity at x = 3 where f(3) = 7. :: The function has a value of f (3), a limit as x approaches 3, but is not continuous at x = 3. :: The function has a limit as x approaches 3, but the function is not defined and is not continuous at x = 3. :: The function has a removable discontinuity at x=3 and an infinite discontinuity at x= -3.
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Chapter 12 Solutions

Calculus For The Life Sciences

Ch. 12.1 - YOUR TURN Write the elements belonging to the set...Ch. 12.1 - Prob. 2YTCh. 12.1 - Prob. 3YTCh. 12.1 - Prob. 4YTCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - In Exercises 1-6, write true or false for each...Ch. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6E
Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - What does the notation n(A) represent?Ch. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - Prob. 60ECh. 12.1 - Draw a Venn diagram and use the given information...Ch. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.1 - Prob. 77ECh. 12.1 - Prob. 78ECh. 12.1 - Prob. 79ECh. 12.1 - Military The number of female military personal in...Ch. 12.1 - Chinese New Year A survey of people attending a...Ch. 12.1 - Prob. 86ECh. 12.1 - Prob. 87ECh. 12.1 - Prob. 88ECh. 12.1 - Prob. 89ECh. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Prob. 93ECh. 12.2 - YOUR TURN 1 Two coins are tossed, and a head or a...Ch. 12.2 - Prob. 2YTCh. 12.2 - Prob. 3YTCh. 12.2 - Prob. 4YTCh. 12.2 - Prob. 5YTCh. 12.2 - Prob. 6YTCh. 12.2 - YOUR TURN 7 Find the probability that when two...Ch. 12.2 - Prob. 8YTCh. 12.2 - Prob. 9YTCh. 12.2 - Prob. 10YTCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Write the sample space for the experiments in...Ch. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - For the experiments in Exercises 9-14, write out...Ch. 12.2 - Prob. 12ECh. 12.2 - For the experiments in Exercises 9-14,write out...Ch. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - EXERCISES Decide whether the events in Exercises...Ch. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - EXERCISES Two dice are rolled. Find the...Ch. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - The numbers 1, 2, 3, 4, and 5 are written on slips...Ch. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - EXERCISES Which of Exercises 5964are examples of...Ch. 12.2 - EXERCISES Which of Exercises 5964are examples of...Ch. 12.2 - Prob. 61ECh. 12.2 - Prob. 62ECh. 12.2 - Which of Exercises 59-64 are examples of empirical...Ch. 12.2 - Which of Exercises 59-64 are examples of empirical...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Prob. 69ECh. 12.2 - Prob. 70ECh. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - Prob. 80ECh. 12.2 - The following description of the classic Linda...Ch. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Prob. 84ECh. 12.2 - Body Types A study on body types gave the...Ch. 12.2 - Prob. 86ECh. 12.2 - Prob. 87ECh. 12.2 - Prob. 88ECh. 12.2 - Prob. 89ECh. 12.2 - Doctor VisitThe probability that a visit to a...Ch. 12.2 - Shoulder InjuriesAmong a large group of patients...Ch. 12.2 - Prob. 92ECh. 12.2 - Prob. 93ECh. 12.2 - Prob. 94ECh. 12.2 - Prob. 95ECh. 12.2 - Prob. 96ECh. 12.2 - Book of Odds The following table gives the...Ch. 12.2 - Prob. 98ECh. 12.2 - Prob. 99ECh. 12.2 - Civil War Estimates of the Confederate Armys...Ch. 12.2 - Prob. 101ECh. 12.2 - Prob. 103ECh. 12.2 - Prob. 104ECh. 12.2 - Refugees In a refugee camp in southern Mexico it...Ch. 12.2 - Prob. 106ECh. 12.2 - Chinese New Year Exercise 83 of the previous...Ch. 12.2 - Prob. 108ECh. 12.3 - Your turn 1 In example 2, find P(A|F). EXAMPLE 2...Ch. 12.3 - Prob. 2YTCh. 12.3 - Prob. 3YTCh. 12.3 - YOUR TURN At a local college, 4/5 of the students...Ch. 12.3 - Prob. 6YTCh. 12.3 - Prob. 7YTCh. 12.3 - YOUR TURN 8 The probability that a student will...Ch. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - If two fair dices are rolled, find the...Ch. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - If two cards are drawn without replacement from an...Ch. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Decide whether the following pairs of events are...Ch. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Another friend asks you to explain how to tell...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - If A and B are events such that P(A)=0.5 and...Ch. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - The following problem submitted by Daniel Hahn of...Ch. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - The following table shows frequencies for...Ch. 12.3 - Prob. 49ECh. 12.3 - Prob. 51ECh. 12.3 - Breast Cancer To explain why the chance of a woman...Ch. 12.3 - Cigarette Smokers The following table gives a...Ch. 12.3 - Prob. 55ECh. 12.3 - Prob. 56ECh. 12.3 - Prob. 57ECh. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - Prob. 61ECh. 12.3 - Prob. 62ECh. 12.3 - Seat Belt Effectiveness A federal study showed...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Working Women A survey has shown that 52 of the...Ch. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Drivers License Test The Motor Vehicle Department...Ch. 12.3 - Prob. 74ECh. 12.3 - Studying A teacher has found that the probability...Ch. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Alcohol Abstinence The Harvard School of Public...Ch. 12.3 - Prob. 80ECh. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Job QualificationsOf all the people applying for a...Ch. 12.3 - Prob. 85ECh. 12.3 - Prob. 86ECh. 12.4 - Prob. 1YTCh. 12.4 - Prob. 2YTCh. 12.4 - Prob. 3YTCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 4ECh. 12.4 - Draw a histogram for the following, and shade the...Ch. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Find the expected value and standard deviation for...Ch. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Suppose a die is rolled 4 times. a. Find the...Ch. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Four slips of paper numbered 2, 3, 4, and 5 are in...Ch. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.CR - Determine whether each of the following statements...Ch. 12.CR - Prob. 2CRCh. 12.CR - Prob. 3CRCh. 12.CR - Prob. 4CRCh. 12.CR - Prob. 5CRCh. 12.CR - Prob. 6CRCh. 12.CR - Prob. 7CRCh. 12.CR - Prob. 8CRCh. 12.CR - Prob. 9CRCh. 12.CR - Prob. 10CRCh. 12.CR - Prob. 11CRCh. 12.CR - Prob. 12CRCh. 12.CR - Prob. 13CRCh. 12.CR - Prob. 14CRCh. 12.CR - Prob. 15CRCh. 12.CR - Prob. 16CRCh. 12.CR - Prob. 17CRCh. 12.CR - Prob. 18CRCh. 12.CR - Prob. 19CRCh. 12.CR - Prob. 20CRCh. 12.CR - Prob. 21CRCh. 12.CR - Prob. 22CRCh. 12.CR - Prob. 23CRCh. 12.CR - Prob. 24CRCh. 12.CR - Prob. 25CRCh. 12.CR - Prob. 26CRCh. 12.CR - Prob. 27CRCh. 12.CR - Prob. 28CRCh. 12.CR - Prob. 29CRCh. 12.CR - Prob. 30CRCh. 12.CR - Prob. 31CRCh. 12.CR - Prob. 32CRCh. 12.CR - Prob. 33CRCh. 12.CR - Prob. 34CRCh. 12.CR - Prob. 35CRCh. 12.CR - Prob. 36CRCh. 12.CR - Prob. 37CRCh. 12.CR - Prob. 38CRCh. 12.CR - Prob. 39CRCh. 12.CR - Prob. 40CRCh. 12.CR - Prob. 41CRCh. 12.CR - Prob. 42CRCh. 12.CR - Prob. 43CRCh. 12.CR - Prob. 44CRCh. 12.CR - Prob. 45CRCh. 12.CR - Prob. 46CRCh. 12.CR - Prob. 47CRCh. 12.CR - Prob. 48CRCh. 12.CR - Prob. 49CRCh. 12.CR - Prob. 50CRCh. 12.CR - Prob. 51CRCh. 12.CR - Prob. 52CRCh. 12.CR - Prob. 53CRCh. 12.CR - Prob. 54CRCh. 12.CR - Prob. 55CRCh. 12.CR - Prob. 56CRCh. 12.CR - Prob. 57CRCh. 12.CR - Prob. 58CRCh. 12.CR - Prob. 59CRCh. 12.CR - Prob. 60CRCh. 12.CR - Prob. 61CRCh. 12.CR - Prob. 62CRCh. 12.CR - Prob. 63CRCh. 12.CR - Prob. 64CRCh. 12.CR - Prob. 65CRCh. 12.CR - Prob. 66CRCh. 12.CR - Prob. 67CRCh. 12.CR - Prob. 68CRCh. 12.CR - Prob. 69CRCh. 12.CR - Prob. 70CRCh. 12.CR - Prob. 71CRCh. 12.CR - Prob. 72CRCh. 12.CR - Prob. 73CRCh. 12.CR - Prob. 74CRCh. 12.CR - Prob. 75CRCh. 12.CR - Prob. 76CRCh. 12.CR - Prob. 77CRCh. 12.CR - Prob. 78CRCh. 12.CR - Prob. 79CRCh. 12.CR - Prob. 80CRCh. 12.CR - Prob. 81CRCh. 12.CR - Prob. 82CRCh. 12.CR - Prob. 83CRCh. 12.CR - Prob. 84CRCh. 12.CR - Prob. 85CRCh. 12.CR - Prob. 86CRCh. 12.CR - Prob. 87CRCh. 12.CR - Prob. 88CRCh. 12.CR - Prob. 89CRCh. 12.CR - Prob. 90CRCh. 12.CR - Prob. 91CRCh. 12.CR - Prob. 92CRCh. 12.CR - Prob. 93CRCh. 12.CR - Prob. 94CRCh. 12.CR - Prob. 97CRCh. 12.CR - Body Mass Index the results of a survey of body...Ch. 12.CR - Elections In the 2012 presidential election, over...Ch. 12.CR - Prob. 105CRCh. 12.CR - Prob. 109CRCh. 12.CR - Prob. 110CRCh. 12.CR - Prob. 112CRCh. 12.EA - Find P(H2C1).Ch. 12.EA - Prob. 2EACh. 12.EA - Prob. 3EA
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