Question 1

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, since they are mutually exclusive. The probability of rolling a 3 is $\frac{1}{6}$, and the probability of rolling a 5 is also $\frac{1}{6}$. Therefore, the total probability is $\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.

Question 2

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 3

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

Accepted Answer

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

Question 4

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

The probability is the number of people struck by lightning divided by the total population. 
So, 304/300,000,000 = 0.00000101, which is closest to option B.

Question 5

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...

Question 6

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 happen independently of each other.

Question 7

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 at least one engine has a defect, as it represents all other possible outcomes that are not the original event.

Question 8

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 can be calculated as (1/365) x (1/365) x (1/365) = 0.00000751, which is closest to option C.

Question 9

Which of the following statements is not true?

Accepted Answer

The statement "If the probability of an event occurring is 1.5, then it is certain that event will occur" is not true. Probability values can never exceed 1, and a probability of 1 means that the event is certain to occur.

Question 10

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 answer of Results from a marijuana drug test study...

Question 11

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, resulting in 3x3=9 total combinations. Option D lists all unique pairings, including same-candy pairs (LD-LD, CD-CD, LP-LP) and different-candy pairs in both possible orders (e.g., LD-CD and CD-LD).

Question 12

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 13

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. $$\begin{array} { | l | l | } 
\hline \begin{array} { l } 
\text { Waiting Time } \
\text { (minutes) }
\end{array} & \begin{array} { l } 
\text { Number of } \
\text { Custemers }
\end{array} \
\hline 0 - 3 & 9 \
\hline 4 - 7 & 10 \
\hline 8 - 11 & 12 \
\hline 12 - 15 & 4 \
\hline 16 - 19 & 4 \
\hline 20 - 23 & 2 \
\hline 24 - 27 & 2 \
\hline
\end{array}$$ 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 0.273 (4 + 4 + 2 + 2 / 43). The probability that the waiting time is between 8 and 15 minutes is 0.384 (12 + 4 / 43). The probability that the waiting time is at least 12 minutes or between 8 and 15 minutes is 0.558 (0.273 + 0.384 - 0.093).

Question 14

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 15

Refer to the table which summarizes the results of testing for a certain disease. $$\begin{array} { l | c c } 
& \begin{array} { l } 
\text { Positive } \
\text { Test Result }
\end{array} & \begin{array} { l } 
\text { Negative } \
\text { Test Result }
\end{array} \
\hline \text { Subject has the disease } & 87 & 9 \
\text { Subject does not have the disease } & 27 & 312
\end{array}$$ 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 P(A|B) = P(A and B) / P(B), where A is the event that the subject has the disease and B is the event of a negative test result. Here, P(A and B) = 9 (subjects who have the disease and tested negative) and P(B) = 9 + 312 (all subjects who tested negative). Thus, P(A|B) = 9 / (9 + 312) = 9 / 321 = 0.028.

Question 16

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

The two events are disjoint because you cannot have a full-time day job as a teller with a bank and a full-time day job as a cashier at a store at the same time. Choosing one precludes the possibility of the other.

Question 17

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 odds used for determining the payoff are defined as the ratio of the probability of winning to the probability of losing. 
In this case, the probability of winning is the chance of the certain event happening, which is not given in the problem. However, we can use the payoff ratio to determine the implied probability of winning.

The payoff ratio is $115:$5 or 23:1. This means that for every $1 bet, the payoff is $23 (including the original $1 bet). Therefore, the implied probability of winning is 1/(23+1) = 1/24.

The odds used for determining the payoff is the ratio of the probability of winning to the probability of losing, which is (1/24):(23/24) or 1:22.

Therefore, the correct choice is C) 22:1.

Question 18

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 19

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 probability that a person drinks root beer given that they are over 40 is calculated by dividing the number of people over 40 who prefer root beer (30) by the total number of people over 40 (20 + 30 + 35 = 85). Thus, the probability is 30/85, which simplifies to 6/17.

Question 20

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

0.741To 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(T) = 0.93 (probability of telling the truth)- P(F|~T) = 0.65 (probability of failing the test given the person lied)- P(~T) = 0.07 (probability of lying, which is 1 - P(T))We can calculate P(F), the total probability of failing the test, using the law of total probability:P(F) = P(F|T)P(T) + P(F|~T)P(~T)     = 0.14*0.93 + 0.65*0.07     = 0.1302 + 0.0455     = 0.1757Now, using Bayes' theorem:P(T|F) = [P(F|T)P(T)] / P(F)       = (0.14*0.93) / 0.1757       = 0.1302 / 0.1757       ≈ 0.741Therefore, the probability that a person who fails the test was actually telling the truth is approximately 0.741.

Quiz 4: Probability

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

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.

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

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.

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

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

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.

Which of the following statements is not true?

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?

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.

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?

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.

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.

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.

Quiz 4: Probability

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

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.

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

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.

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

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

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.

Which of the following statements is not true?

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?

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.

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?

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.

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.

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.

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