Question 1

The table below describes the smoking habits of a group of asthma sufferers.
 $\begin{array}{r|crrr} 
&&\text { Light}&\text { Heavy }\
& \text { Nonsmoker } & \text { smoker} & \text { smoker } & \text { Total } \
\hline \text { Men } & 385 & 77 & 77 & 539 \
\text { Women } & 350 & 70 & 67 & 487 \
\text { Total } & 735 & 147 & 144 & 1026
\end{array}$
 If one of the 1026 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker. Round to the nearest thousandth.
A) 0.476
B) 0.068
C) 0.243
D) 0.144

Accepted Answer

The probability that the person chosen is a woman given that the person is a light smoker is calculated by dividing the number of women who are light smokers by the total number of light smokers: $ \frac{70}{147} \approx 0.476 $.

Question 2

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-If a person told you in what month he was born, would it be "unusual" to guess the date of his birth (not including the year)?
A) Yes
B) No

Accepted Answer

Given only the month someone is born, guessing the exact date of birth is challenging due to the multiple possibilities (28-31 days depending on the month). This makes it statistically unusual to correctly guess the specific date without additional information.

Question 3

Refer to the table which summarizes the results of testing for a certain disease. $$\begin{array} { l | c c } 
& \text { Positive Test Result } & \text { Negative Test Result } \
\hline \text { Subject has the disease } & 119 & 6 \
\text { Subject does not have the disease } & 13 & 177
\end{array}$$ 
If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test?
A) 0.0413; The probability of this error is low so the test is fairly accurate.
B) 0.581; The probability of this error is high so the test is not very accurate.
C) 0.0190; The probability of this error is low so the test is fairly accurate.
D) 0.0480; The probability of this error is low so the test is fairly accurate.

Accepted Answer

The probability of a false negative is calculated as the number of false negatives (6) divided by the total number of tests (315). This gives 6/315 = 0.0190, indicating a low probability of this error, suggesting the test is fairly accurate.

Question 4

Is Event B dependent or independent of Event A?
-A: You cook your chicken improperly. 
B: You get salmonella poisoning.

A) Independent
B) Dependent

Accepted Answer

Event B is dependent on Event A because getting salmonella poisoning can be a direct result of cooking chicken improperly.

Question 5

Suppose you are playing a game of chance. If you bet $4 on a certain event, you will collect $184 (including your $4 bet) if you win. Find the odds used for determining the payoff.
A) 1 : 45
B) 184 : 188
C) 45 : 1
D) 46 : 1

Accepted Answer

The odds are calculated as the ratio of the net gain to the bet amount. The net gain is $184 - $4 = $180. Therefore, the odds are $180 : $4, which simplifies to 45 : 1.

Question 6

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-If you drew one card from a standard deck, would it be "unusual" to draw an ace of diamonds?
A) Yes
B) No

Accepted Answer

The answer of Answer the question, considering an event to...

Question 7

Express the indicated degree of likelihood as a probability value.
-"You have one chance in ten of winning the race."
A) 1
B) 0.90
C) 0.5
D) 0.10

Accepted Answer

The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Here, the probability is 1 chance in 10, which is 1/10 or 0.10.

Question 8

12 wrestlers compete in a competition. If each wrestler wrestles one match with each other wrestler, what are the total numbers of matches?
A) 156
B) 78
C) 66
D) 132

Accepted Answer

The total number of matches is given by the combination formula C(n, 2), where n is the number of wrestlers. For 12 wrestlers, it's C(12, 2) = 12 * 11 / 2 = 66 matches.

Question 9

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-Is it "unusual" to get a 12 when a pair of dice is rolled?
A) Yes
B) No

Accepted Answer

The probability of rolling a 12 with two dice is 1/36, which is approximately 0.0278. Since this is less than 0.05, it is considered "unusual."

Question 10

How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?
A) 48
B) 40,320
C) 720
D) 20,160

Accepted Answer

The number of ways to choose and arrange 6 people out of 8 is given by the permutation formula: P(n, r) = n! / (n-r)!. Here, n = 8 and r = 6, so P(8, 6) = 8! / (8-6)! = 8! / 2! = 40,320 / 2 = 20,160.

Question 11

Find the indicated complement.
-The probability that Luis will pass his statistics test is 0.67. Find the probability that he will fail his statistics test.
A) 1.49
B) 0.34
C) 2.03
D) 0.33

Accepted Answer

The complement of an event is the probability of the event not happening. So, the probability that Luis will fail his statistics test is 1 - 0.67 = 0.33.

Question 12

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of
Them are acceptable.
A) 0.343
B) 0.429
C) 2.1
D) 0.027

Accepted Answer

The probability that all three products are acceptable is calculated by multiplying the probability of one product being acceptable (0.7) three times: 0.7 * 0.7 * 0.7 = 0.343.

Question 13

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The table below shows the soft drinks preferences of people in three age groups. 
$$\begin{array} { r | c c c } 
& \text { cola } & \text { root beer } & \text { lemon-lime } \
\hline \text { under 21 years of age } & 40 & 25 & 20 \
\text { between 21 and 40 } & 35 & 20 & 30 \
\text { over 40 years of age } & 20 & 30 & 35
\end{array}$$ 
If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40. 
A) $\frac { 6 } { 17 }$

B) $\frac { 2 } { 17 }$

C) $\frac { 2 } { 5 }$

D) None of the above is correct.

Accepted Answer

The probability that the person drinks root beer given that they are over 40 is the number of people who drink root beer and are over 40 divided by the total number of people who are over 40. From the table, we see that there are 30 people who drink root beer and are over 40, and there are 85 people who are over 40. Therefore, the probability that the person drinks root beer given that they are over 40 is 30/85 = 6/17.

Question 14

A state lottery involves the random selection of six different numbers between 1 and 26. If you 125) select one six number combination, what is the probability that it will be the winning combination?

A) $\frac { 1 } { 230,230 }$

B) $\frac { 1 } { 308,915,776 }$

C) $\frac { 1 } { 720 }$

D) $\frac { 1 } { 165,765,600 }$

Accepted Answer

The total number of ways to choose 6 different numbers from 26 is given by the combination formula $\binom{26}{6}$, which equals 230,230. Therefore, the probability of selecting the winning combination is $\frac{1}{230,230}$.

Question 15

A multiple choice question has 12 possible answers, only one of which is correct. Is it "unusual" to answer a question correctly if a random guess is made?

Accepted Answer

The answer of A multiple choice question has 12 possible...

Question 16

In a poll, respondents were asked whether they had ever been in a car accident. 353 respondents indicated that they had been in a car accident and 499 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth, if necessary.
A) 0.707
B) 0.586
C) 0.003
D) 0.414

Accepted Answer

The probability is calculated by dividing the number of respondents who have been in a car accident (353) by the total number of respondents (353 + 499 = 852). So, the probability is 353/852 ≈ 0.414.

Question 17

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The following table contains data from a study of two airlines which fly to Small Town, USA. $$\begin{array} { c | c c } 
& \text { Number of flights} & \text { Number of flights } \
& \text { which were on time } & \text { which were late } \
\hline \text { Podunk Airlines } & 33 & 6 \
\text { Upstate Airlines } & 43 & 5
\end{array}$$
 If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time. 
A) $\frac { 43 } { 76 }$

B) $\frac { 43 } { 87 }$

C) $\frac { 11 } { 76 }$

D) None of the above is correct.

Accepted Answer

The probability of selecting an Upstate Airlines flight is 43/87, and the probability of selecting a flight that was on time is 48/87. The probability of selecting an Upstate Airlines flight that was on time is (43/87) * (48/87) = 43/87.

Question 18

Evaluate the expression.

-8!
A) 5040
B) 40,312
C) 40,328
D) 40,320

Accepted Answer

The factorial of 8 (8!) is calculated as 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 40,320.

Question 19

Use Bayes' theorem to find the indicated probability.
-Use the results summarized in the table. $$\begin{array} { l | c c } 
& \text { Approve of mayor } & \text { Do not approve of mayor } \
\hline \text { Republican } & 15 & 13 \
\text { Democrat } & 20 & 17 \
\text { Independent } & 12 & 23
\end{array}$$
 One of the 100 test subjects is selected at random. Given that the person selected approves of the mayor, what is the probability that they vote Democrat?
A) 0.313
B) 0.578
C) 0.426
D) 0.541

Accepted Answer

The probability that a person approves of the mayor and is a Democrat is 20/100. The probability that a person approves of the mayor is (15+20+12)/100 = 47/100. Using Bayes' theorem, the probability that a person is a Democrat given they approve of the mayor is (20/100) / (47/100) = 20/47 ≈ 0.426.

Question 20

Find the indicated probability.
-A sample of 4 different calculators is randomly selected from a group containing 48 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places.
A) 0.0301
B) 0.2389
C) 0.2483
D) 40.1610

Accepted Answer

The answer of Find the indicated probability.
-A sample of 4...

Quiz 4: Probability

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -If a person told you in what month he was born, would it be "unusual" to guess the date of his birth (not including the year) ?

Is Event B dependent or independent of Event A? -A: You cook your chicken improperly. B: You get salmonella poisoning.

Suppose you are playing a game of chance. If you bet $4 on a certain event, you will collect $184 (including your $4 bet) if you win. Find the odds used for determining the payoff.

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

Express the indicated degree of likelihood as a probability value. -"You have one chance in ten of winning the race."

12 wrestlers compete in a competition. If each wrestler wrestles one match with each other wrestler, what are the total numbers of matches?

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Is it "unusual" to get a 12 when a pair of dice is rolled?

How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

Find the indicated complement. -The probability that Luis will pass his statistics test is 0.67. Find the probability that he will fail his statistics test.

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of Them are acceptable.

A state lottery involves the random selection of six different numbers between 1 and 26. If you 125) select one six number combination, what is the probability that it will be the winning combination?

A multiple choice question has 12 possible answers, only one of which is correct. Is it "unusual" to answer a question correctly if a random guess is made?

Evaluate the expression. -8!

Find the indicated probability. -A sample of 4 different calculators is randomly selected from a group containing 48 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places.