Section 3 Homework

Find​ P(A or B or​ C) for the given probabilities. P(A) = 0.34, P(B) = 0.27, P(C) = 0.11 P(A and B) = 0.12, P(A and C) = 0.03, P(B and C) = 0.07 P(A and B and C) = 0.01 P(A or B or C) = *___*

Correct Answer: *0.51*

A physics class has 50 students. Of​ these, 13 students are physics majors and 17 students are female. Of the physics​ majors, three are female. Find the probability that a randomly selected student is female or a physics major. (Round to *three* decimal places.) The probability that a randomly selected student is female or a physics major is *____*.

Correct Answer: *0.540*

Of the cartons produced by a​ company, 7​% have a​ puncture, 10​% have a smashed​ corner, and 1.1​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. (Type as an *integer (whole number)* or a *decimal*. *DO NOT ROUND*.) The probability that a randomly selected carton has a puncture or a smashed corner *____%*.

Correct Answer: *15.9%*

Can two events with nonzero probabilities be both independent and mutually​ exclusive? Choose the correct answer below. A.) No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero. B.) ​Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities add up to one. C.) ​Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal. D.) No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.

Correct Answer: A.) No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. *If two events are mutually​ exclusive, they have no outcomes in common.* Choose the correct answer below. A.) False. If two events are mutually​ exclusive, they have every outcome in common. B.) True. C.) False. If two events are mutually​ exclusive, they have some outcomes in common.

Correct Answer: B.) True.

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)*. Choose the correct answer below. A.) ​False, the probability that A or B will occur is P(A or B) = P(A) + P(B). B.) ​False, the probability that A or B will occur is P(A or B) = P(A) × P(B). C.) True D.) False, the probability that A or B will occur is P(A or B) = P(A) + P(B) − P(A and B).

Correct Answer: D.) False, the probability that A or B will occur is P(A or B) = P(A) + P(B) − P(A and B).

If two events are mutually​ exclusive, why is P(A and B) = 0​? Choose the correct answer below. A.) P(A and B) = 0 because A and B are independent. B.) P(A and B) = 0 because A and B are complements of each other. C.) P(A and B) = 0 because A and B each have the same probability. D.) P(A and B) = 0 because A and B cannot occur at the same time.

Correct Answer: D.) P(A and B) = 0 because A and B cannot occur at the same time.

Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. (Since I don't have Quizlet+, I can't insert the image of the actual Venn Diagram; ergo, I pasted the description.) Sample​ Space: Presidential Candidates *Blue* bubble (A): Presidential candidates who were over 60 years old *Pink* bubble (B): Presidential candidates who won the election *Purple* overlap: (A) and (B) The events *__(1)__* mutually​ exclusive, since there *______(2)______* and *_____(3)_____*.

Correct Answers: *(1):* *are not* *(2):* *is at least 1 presidential candidate who was over 60 years old* *(3):* *won the election.*

Determine whether the following events are mutually exclusive. Explain your reasoning. *Event​ A: Randomly select a female biology major.* *Event​ B: Randomly select a biology major who is 19 years old.* These events *___(1)___* mutually​ exclusive, since *__________(2)__________*.

Correct Answers: *(1):* *are not* *(2):* *it is possible to select a female biology major who is 19 years old.*

Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. Sample​ Space: Movies *Blue* bubble (A): Movies that are rated R *Pink* bubble (B): Movies that make less than $20 million *Purple* overlap: (A) and (B) The events *___(1)___* mutually​ exclusive, since there are *__(2)__* movies that are rated R and *_____(3)_____*.

Correct Answers: *(1):* *are not* *(2):* *some* *(3):* *make less than $20 million.*

Determine whether the following events are mutually exclusive. Explain your reasoning. *Event​ A: Randomly select a voter who legally voted for the President in New Hampshire.* *Event​ B: Randomly select a voter who legally voted for the President in California.* These events *___(1)___* mutually​ exclusive, since it *____(2)____* possible for a voter to both have legally voted for the President in New Hampshire and *___(3)___* legally voted for the President in California.

Correct Answers: *(1):* *are* *(2):* *is not* *(3):* *have*

The table below shows the results of a survey that asked 2845 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts​ 1 (a) through​ 4 (d) (round answers to the *nearest thousandth*). *Frequently (I)* *Occasionally (II)* *Not at all (III)* *Total ("IV")* *Male:* *(I):* *222* *(II):* *453* *(III):* *792* *("IV"):* *"1467"* *Female:* *(I):* *204* *(II):* *430* *(III):* *744* *("IV"):* *"1378"* *Total:* *(I):* *426* *(II):* *883* *(III):* *1536* *("IV"):* *"2845"* *Part 1 (a):* Find the probability that the person is frequently or occasionally involved in charity work. P(being frequently involved or being occasionally involved) = *____* *Part 2 ​(b):* Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved) = *____* *Part 3 (c):* Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved) = *____* *Part 4 ​(d):* Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved) = *____*

Correct Answers: *Part 1 (a)*: *0.460* *Part 2 (b)*: *0.763* *Part 3 (c)*: *0.587* *Part 4 (d)*: *0.922*

A standard deck of cards contains 52 cards. One card is selected from the deck. (Round answers to *three* decimal places). ​ *Part 1 (a)*: Compute the probability of randomly selecting an eight or nine. ​*Part 2 (b)*: Compute the probability of randomly selecting an eight or nine or seven. ​*Part 3 (c)*: Compute the probability of randomly selecting a three or diamond. *Part 1 (a):*​ P(eight or nine​) = *____* *Part 2 (b):*​ P(eight or nine or seven) = *____* *Part 3 (c):* P(three or diamond) = *____*

Correct Answers: *Part 1 (a):* *0.154* *Part 2 (b):* *0.231* *Part 3 (c):* *0.308*

The responses of 977 adults in a certain region to a survey question about the story of​ Britons' vote to leave the European Union are shown in the accompanying Pareto chart. Find the probability of each event listed in parts​ 1 (a) through​ 4 (d) below (type answers as either an *integer* or a *decimal, and round to *three* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual Pareto Chart; ergo, I pasted the description.) A Pareto Chart, with vertical bars, entitled *"How Important is the Brexit Story to You Personally?"* has a horizontal axis labeled *"Response"* with tick marks labeled *C*, *B*, *D*, *E*, *A*, and *F*, and a vertical axis labeled *"Number responding"* from *0 to 360* in *increments of "40"*. The horizontal axis *"key"* is as follows: *A* means *Extremely important*, *B* means *Very important*, *C* means *Somewhat important*, *D* means *Not too important*, *E* means *Not at all important*, and *F* means *Did not answer*. The chart has 6 bars of equal width with horizontal axis labels and labeled heights as follows from *left to right*: *(C, 310); (B, 221); (D, 194); (E, 128); (A, 90); (F, 34)*. *Part 1 ​(a):* Randomly selecting an adult who thinks the story is somewhat important The probability is *____*. *Part 2 ​(b):* Randomly selecting an adult who thinks the story is not at all important The probability is *____*. *Part 3 ​(c):* Randomly selecting an adult who thinks the story is not too important or not at all important The probability is *____*. *Part 4 ​(d):* Randomly selecting an adult who thinks the story is extremely important or very important The probability is *____*.

Correct Answers: *Part 1 (a):* *0.317* *Part 2 (b):* *0.131* *Part 3 (c):* *0.330* *Part 4 (d):* *0.318*

You roll a​ six-sided die. Find the probability of each of the following scenarios. (Round answers to *three* decimal places). ​*Part 1 (a):* Rolling a 6 or a number greater than 3 *Part 2 ​(b):* Rolling a number less than 4 or an even number *Part 3 ​(c):* Rolling a 2 or an odd number *Part 1 ​(a):* ​P(6 or number > 3) = *____* *Part 2 ​(b):* P(1 or 2 or 3 or 4 or ​6) = *____* *Part 3 ​(c):* ​P(2 or 1 or 3 or​ 5) = *____*

Correct Answers: *Part 1 (a):* *0.500* *Part 2 (b):* *0.833* *Part 3 (c):* *0.667*

The accompanying table shows the numbers of male and female students in a certain region who received​ bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts​ 1 (a) through​ 3 (c) below (type answers as either an *integer* or a *decimal*, and round to *three* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual table; ergo, I pasted the information (information in parenthesis are for the last part of the table).) *Degrees in Field* (*D.F.*), *Degrees Outside of Field* (*D.o.F.*), *Total* (*"G.T."*) *Males*: *173,920*, *609,851*, *783,771* *Females*: *127,757*, *893,534*, *1,021,291* *Total*: *D.F.:* *301,677* *D.o.F.:* *1,503,385* *"G.T.":* *1,805,062* *Part 1 (a):* The student is male or received a degree in the field The probability is *____*. ​ *Part 2 ​(b):* The student is female or received a degree outside of the field The probability is *____*. *Part 3 (c):* The student is not female or received a degree outside of the field The probability is *____*.

Correct Answers: *Part 1 (a):* *0.505* *Part 2 (b):* *0.904* *Part 3 (c):* *0.929*

The responses of 1443 voters to a survey about the way the media conducted themselves in a recent political campaign are shown in the accompanying Pareto chart. Find the probability of each event listed in parts​ 1 (a) through​ 4 (d) below (type answers as either as an *integer* or a *decimal*, and round to *three* decimal places). (Since I don't have Quizlet+, I can't insert the image of the actual Pareto Chart; ergo, I pasted the description). A Pareto Chart entitled *"How Would You Grade the Media for the Way They Conducted Themselves in the Campaign?"* has a horizontal axis labeled *"Response"* with tick marks labeled *F*, *A or B*, *D*, and *C*, and a vertical axis labeled *"Number responding"* from *0 to 650* in *increments of "50"*. The Pareto chart has vertical bars, each of which are centered over a horizontal axis tick mark. The heights of the vertical bars are as follows, where the *Response (letter grade)* is listed *first*, and the *height* is listed *second*: *(F, 584); (A or B, 351); (D, 287); (C, 221)*. *Part 1 (a):* Randomly selecting a person from the sample who did not give the media an A or a B The probability is *____*. *Part 2 (b):* Randomly selecting a person from the sample who gave the media a grade better than a D The probability is *____*. *Part 3 ​(c):* Randomly selecting a person from the sample who gave the media a D or an F The probability is *____*. *Part 4 (d):* Randomly selecting a person from the sample who gave the media a C or a D The probability is *____*.

Correct Answers: *Part 1 (a):* *0.757* *Part 2 (b):* *0.396* *Part 3 (c):* *0.604* *Part 4 (d):* *0.352*

The table below shows the results of a survey that asked 1051 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts​ 1 (a) through​ 3 (c) (round answers to the *nearest thousandth* (*three* decimal places)). *Support (I)*; *Oppose (II)*; *Unsure (III)*; *Total ("IV")* *Males*: *158*; *321*; *6*; *"485"* *Females*: *239*; *305*; *22*; *566* *Total*: *(I):* *397*; *(II):* *626*; *(III): *28*; *("IV"):* *"1051"* *Part 1 (a):* Find the probability that the person opposed the tax or is female. ​P(opposed the tax or is ​female) = *____* *Part 2 ​(b):* Find the probability that the person supports the tax or is male. ​P(supports the tax or is ​male) = *____* *Part 3 (c):* Find the probability that the person is not unsure or is female. ​P(is not unsure or is ​female) = *____*

Correct Answers: *Part 1 (a):* *0.844* *Part 2 (b):* *0.689* *Part 3 (c):* *0.994*

The estimated percent distribution of a certain​ country's population for 2025 is shown in the accompanying pie chart. Find the probability of each event listed in parts​ 1 (a) through​4 (d) below (round answers to *one* decimal place). (Since I don't have Quizlet+, I can't insert the image of the actual pie chart (circle graph); ergo, I pasted the description). A circle graph entitled *"National Age Distribution"* is divided into nine sectors with labels and approximate sizes as a percentage of a circle as follows: *Under 5 years, 4.8%; 5 - 14 years, 12.1%; 15 - 19 years, 5.8%; 20 - 24 years, 6.5%; 25 - 34 years, 12.9%; 35 - 44 years, 13.2%; 45 - 64 years, 26.5%; 65 - 74 years, 10.9%; 75 years or over, 7.2%*. *Part 1 (a):* Randomly selecting someone who is under 5 years old The probability is *___%*. *Part 2 ​(b):* Randomly selecting someone who is 45 years old or over The probability is *___%*. *Part 3 (c):* Randomly selecting someone who is not 65 years old or over The probability is *___%*. *Part 4 ​(d):* Randomly selecting someone who is between 20 and 34 years old The probability is *___%*.

Correct Answers: *Part 1 (a):* *4.8%* *Part 2 (b):* *44.6%* *Part 3 (c):* *81.9%* *Part 4 (d):* *19.4%*

The percent of college​ students' marijuana use for a sample of 97,227 students is shown in the accompanying pie chart. Find the probability of each event listed in parts​ 1 (a) through​ 4 (d) below (round answers to *one* decimal place). (Since I don't have Quizlet+, I can't insert the image of the actual pie chart (circle graph); ergo, I pasted the description.) A circle graph entitled *"Marijuana Use in the Last 30 Days"* is divided into five sectors with labels and approximate sizes as a percentage of a circle as follows: *Never used, 56.4%; Used, but not in the last 30 days, 25.0%; Used 1 - 9 days, 10.0%; Used 10 - 29 days, 5.0%; Used all 30 days, 3.6%*. *Part 1 (a):* Randomly selecting a student who never used marijuana The probability is *___%*. *Part 2 (b):* Randomly selecting a student who used marijuana The probability is *___%*. *Part 3 (c):* Randomly selecting a student who used marijuana between 1 and 29 of the last 30 days The probability is *___%*. *Part 4 (d):* Randomly selecting a student who used marijuana on at least 1 of the last 30 days The probability is *___%*.

Correct Answers: *Part 1 (a):* *56.4%* *Part 2 (b):* *43.6%* *Part 3 (c):* *15.0%* *Part 4 (d):* *18.6%*