Question 1

Of the thirteen different women Calvin asks for a date, at least one of them accepts. Provide a written description of the complement of the given event.

Accepted Answer

The complement of at least one woman accepting Calvin's offer is that none of the women accept his offer.

Question 2

The table below shows the soft drinks preferences of people in three age groups $\begin{array}{l|ccc} 
& \text { Cola } & \text { Root Beer } & \text { Lemon-lime } \
\hline \text { Under 21 years of age } & 40 & 25 & 20 \
\text { Between 21 and 40 } & 35 & 20 & 30 \
\text { Over 40 years of age } & 20 & 30 & 35
\end{array}$

If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40 .

Accepted Answer

The answer of The table below shows the soft drinks...

Question 3

When 100 engines are shipped, all of them are free of defects. Select a written description of the complement of the given event.

Accepted Answer

The complement of all engines being free of defects is that there is at least one defective engine, as it represents all other possibilities except the original event.

Question 4

Determine whether the events are disjoint. Finding a ten dollar bill on the sidewalk. Finding a ten dollar bill on the grass.

Accepted Answer

Disjoint events are events that cannot happen at the same time. Finding a ten dollar bill on the sidewalk and finding a ten dollar bill on the grass are not mutually exclusive events; they can occur independently of each other, thus they are not disjoint.

Question 5

If you drew one card from a standard deck, would it be "significant" to draw a 5? Answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.

Accepted Answer

In a standard deck of 52 cards, there are 4 fives. The probability of drawing a five is 4/52, which simplifies to 1/13, approximately 0.077. This is greater than 0.05, so it is not considered "significant" by the given definition.

Question 6

In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Accepted Answer

Odds against an event = (Probability of the event not happening) : (Probability of the event happening) = (1 - P(event)) : P(event). Here, P(commuting by bicycle) = 10% or 0.1, so odds against = (1 - 0.1) : 0.1 = 0.9 : 0.1 = 9 : 1.

Question 7

Find the indicated probability. Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

Accepted Answer

The probability that 3 randomly selected people all have the same birthday, ignoring leap years, is calculated by considering that the first person can have any birthday, the second must have the same birthday as the first (1/365 chance), and the third must also match the first two (1/365 chance). Thus, the probability is (1/365) * (1/365) = 1/133,225 or approximately 0.00000751 when rounded to eight decimal places.

Question 8

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana?

Accepted Answer

The total number of subjects is 143 + 157 = 300. The number of subjects who did not use marijuana includes those with true negative results and false positive results, which is 157 - 3 (true negatives) + 24 (false positives) = 178. Therefore, the probability that a randomly selected subject did not use marijuana is 178 / 300 = 0.593.

Question 9

Fred and Ed each have a bag of candy containing a lemon drop (LD), a cherry drop(CD), and a lollipop (LP). Each takes out a piece from their own bag and eats it. What are the possible pairs of candies eaten?

Accepted Answer

Each person has three choices of candy, and since there are two people, each choice by the first person can be paired with each choice by the second person, resulting in 3x3=9 possible pairs. Option D lists all unique combinations without repetition, covering all possibilities.

Question 10

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. $\begin{array}{|l|l|}
\hline \begin{array}{l}
\text { Waiting Time } \
\text { (minutes) }
\end{array} & \begin{array}{l}
\text { Number of } \
\text { Customers }
\end{array} \
\hline 0-3 & 9 \
\hline 4-7 & 10 \
\hline 8-11 & 12 \
\hline 12-15 & 4 \
\hline 16-19 & 4 \
\hline 20-23 & 2 \
\hline 24-27 & 2 \
\hline
\end{array}$

If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes?

Accepted Answer

The probability that the waiting time is at least 12 minutes is the sum of the probabilities that the waiting time is between 12 and 15 minutes and the probability that the waiting time is between 16 and 19 minutes. The probability that the waiting time is between 12 and 15 minutes is 4/33, and the probability that the waiting time is between 16 and 19 minutes is 4/33. Therefore, the probability that the waiting time is at least 12 minutes is 4/33 + 4/33 = 8/33 = 0.242. The probability that the waiting time is between 8 and 15 minutes is the sum of the probabilities that the waiting time is between 8 and 11 minutes and the probability that the waiting time is between 12 and 15 minutes. The probability that the waiting time is between 8 and 11 minutes is 12/33, and the probability that the waiting time is between 12 and 15 minutes is 4/33. Therefore, the probability that the waiting time is between 8 and 15 minutes is 12/33 + 4/33 = 16/33 = 0.485. The probability that the waiting time is at least 12 minutes or between 8 and 15 minutes is the sum of the probabilities that the waiting time is at least 12 minutes and the probability that the waiting time is between 8 and 15 minutes. Therefore, the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes is 0.242 + 0.485 = 0.727.

Question 11

Evaluate the expression. ${ } _ { 10 } P _ { 3 }$

Accepted Answer

The answer of Evaluate the expression. \({ } _ {...

Question 12

Refer to the table which summarizes the results of testing for a certain disease $\begin{array}{l|cc} 
& \begin{array}{l}
\text { Positive } \
\text { Test Result }
\end{array} & \begin{array}{l}
\text { Negative } \
\text { Test Result }
\end{array} \
\hline \text { Subject has the disease } & 87 & 9 \
\text { Subject does not have the disease } & 27 & 312
\end{array}$

A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative?

Accepted Answer

The probability that a subject has the disease given a negative test result is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event that the subject has the disease, and B is the event of a negative test result. From the table, 9 subjects have the disease and tested negative, and there are a total of 321 negative results (9 + 312). Therefore, the probability is 9/321 = 0.028.

Question 13

A multiple choice question has 18 possible answers, only one of which is correct. "significant" to answer a question correctly if a random guess is made? Consider an event to be "significant" if its probability is less than or equal to 0.05.

Accepted Answer

The probability of guessing the correct answer by chance is 1/18, which is approximately 0.0556. This is greater than 0.05, so it is not considered "significant" by the given definition.

Question 14

Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 65% of lies are identified as lies and that 14% of true statements are also identified as lies. A company gives its job applicants a
Polygraph test, asking "Did you tell the truth on your job application?". Suppose that 93% of
The job applicants tell the truth during the polygraph test. What is the probability that a person
Who fails the test was actually telling the truth?

Accepted Answer

To find the probability that a person who fails the test was actually telling the truth, we use Bayes' theorem. Let's denote T as the event of telling the truth and F as the event of failing the test. We need to find P(T|F), the probability of telling the truth given that the person failed the test.Given:- P(F|T) = 0.14 (probability of failing the test given the person told the truth)- P(F|~T) = 0.65 (probability of failing the test given the person lied)- P(T) = 0.93 (probability of telling the truth)- P(~T) = 0.07 (probability of lying, which is 1 - P(T))Using Bayes' theorem:$$P(T|F) = \frac{P(F|T) \cdot P(T)}{P(F|T) \cdot P(T) + P(F|~T) \cdot P(~T)}$$Substituting the given values:$$P(T|F) = \frac{0.14 \cdot 0.93}{0.14 \cdot 0.93 + 0.65 \cdot 0.07}$$$$P(T|F) = \frac{0.1302}{0.1302 + 0.0455}$$$$P(T|F) = \frac{0.1302}{0.1757} \approx 0.741$$Therefore, the probability that a person who fails the test was actually telling the truth is approximately 0.741.

Question 15

A 6-sided die is rolled. Find P(3  or 5).

Accepted Answer

The probability of rolling a 3 or a 5 on a 6-sided die is the sum of the probabilities of each individual event, which is $\frac{1}{6} + \frac{1}{6} = \frac{1}{3}$, since there is one 3 and one 5 on the die.

Question 16

Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet)if you win. Find the odds used for determining the payoff.

Accepted Answer

The payoff is $115 for a $5 bet, meaning you win $110. The odds are calculated as the amount won ($110) over the amount bet ($5), which simplifies to 22:1.

Question 17

Determine whether the events are disjoint. Get a full-time day job as a teller with a bank. Get a full time day job as a cashier at a store.

Accepted Answer

These events are disjoint because a person cannot simultaneously hold two full-time day jobs at different places.

Question 18

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year.

Accepted Answer

To estimate the probability, divide the number of people struck by lightning (304) by the total population (300,000,000). This gives 304 / 300,000,000 = 0.00000101.

Question 19

Which of the following statements is not true?

Accepted Answer

The probability of an event is defined to be between 0 and 1, inclusive. A probability of 1.5 is not possible, making statement C incorrect.

Question 20

The table below describes the smoking habits of a group of asthma sufferers $$\begin{array} { r | c c c c c } 
& \text { Nonsmoker } & \begin{array} { c } 
\text { Occasional } \
\text { Smoker }
\end{array} & \begin{array} { c } 
\text { Regular } \
\text { Smoker }
\end{array} & \begin{array} { c } 
\text { Heavy } \
\text { Smoker }
\end{array} & \text { Total } \
\hline \text { Men } & 431 & 50 & 71 & 49 & 601 \
\text { Women } & 382 & 48 & 86 & 39 & 555 \
\text { Total } & 813 & 98 & 157 & 88 & 1156
\end{array}$$ If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker.

Accepted Answer

The answer of The table below describes the smoking habits...

Quiz 4: Probability

Of the thirteen different women Calvin asks for a date, at least one of them accepts. Provide a written description of the complement of the given event.

When 100 engines are shipped, all of them are free of defects. Select a written description of the complement of the given event.

Determine whether the events are disjoint. Finding a ten dollar bill on the sidewalk. Finding a ten dollar bill on the grass.

If you drew one card from a standard deck, would it be "significant" to draw a 5? Answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.

In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Find the indicated probability. Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana?

Fred and Ed each have a bag of candy containing a lemon drop (LD) , a cherry drop(CD) , and a lollipop (LP) . Each takes out a piece from their own bag and eats it. What are the possible pairs of candies eaten?

Evaluate the expression. ${ } _ { 10 } P _ { 3 }$

A multiple choice question has 18 possible answers, only one of which is correct. "significant" to answer a question correctly if a random guess is made? Consider an event to be "significant" if its probability is less than or equal to 0.05.

A 6-sided die is rolled. Find P(3 or 5) .

Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet) if you win. Find the odds used for determining the payoff.

Determine whether the events are disjoint. Get a full-time day job as a teller with a bank. Get a full time day job as a cashier at a store.

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year.

Which of the following statements is not true?

Quiz 4: Probability

Of the thirteen different women Calvin asks for a date, at least one of them accepts. Provide a written description of the complement of the given event.

When 100 engines are shipped, all of them are free of defects. Select a written description of the complement of the given event.

Determine whether the events are disjoint. Finding a ten dollar bill on the sidewalk. Finding a ten dollar bill on the grass.

If you drew one card from a standard deck, would it be "significant" to draw a 5? Answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.

In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Find the indicated probability. Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana?

Fred and Ed each have a bag of candy containing a lemon drop (LD) , a cherry drop(CD) , and a lollipop (LP) . Each takes out a piece from their own bag and eats it. What are the possible pairs of candies eaten?

Evaluate the expression. 10P3{ } _ { 10 } P _ { 3 }10​P3​

A multiple choice question has 18 possible answers, only one of which is correct. "significant" to answer a question correctly if a random guess is made? Consider an event to be "significant" if its probability is less than or equal to 0.05.

A 6-sided die is rolled. Find P(3 or 5) .

Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet) if you win. Find the odds used for determining the payoff.

Determine whether the events are disjoint. Get a full-time day job as a teller with a bank. Get a full time day job as a cashier at a store.

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year.

Which of the following statements is not true?

Evaluate the expression. ${ } _ { 10 } P _ { 3 }$