Question 1

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-Is it unlikely to get 11 when a pair of dice is rolled?
A) Yes
B) No

Accepted Answer

The probability of rolling an 11 with a pair of dice is 1/18, which is approximately 0.0556. This is greater than 0.05, so it is not considered unlikely.

Question 2

Estimate the probability of the event.
-A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 0 = FOR, 1 = AGAINST. If the
Referendum were held today, estimate the probability that it would pass. $$0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0$$
A) 0.6
B) 0.65
C) 0.5
D) 0.4

Accepted Answer

The probability of the event is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the number of responses that are "FOR" (0), and the total number of possible outcomes is the total number of responses. There are 10 responses that are "FOR" and 10 responses that are "AGAINST", so the probability of the event is 10/20 = 0.6.

Question 3

From the information provided, create the sample space of possible outcomes.
-Flip a coin three times. 
A) HHH HHT HTH HTT THH THT TTH TTT
B) HHH HTT HTH TTT HTT THH HHT THT
C) HTT THT HTH HHH TTH TTT
D) HHH TTT THT HTH HHT TTH HTH

Accepted Answer

Sample space A includes all possible outcomes of three coin flips, with each flip having two possible outcomes (heads or tails). This means there are 2x2x2=8 possible outcomes in total, which are all listed in option A.

Question 4

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

Accepted Answer

There are 52 cards in a standard deck, and only 1 of them is the ace of hearts. Therefore, the probability of drawing an ace of hearts is 1/52, which is less than 0.05, making it an unlikely event.

Question 5

From the information provided, create the sample space of possible outcomes.
-Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten? 
A) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP
B) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD
C) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD
D) CD-LD LD-LP LP-CD LP-LP LD-LD

Accepted Answer

Each person can choose any of the three candies, so there are 3 possibilities for the first person and 3 possibilities for the second person, giving a total of 3 x 3 = 9 possible pairs of candies. These pairs can be represented by LD-LD, LD-CD, LD-LP, CD-LD, CD-CD, CD-LP, LP-LD, LP-CD, and LP-LP. Out of the given choices, only Option C includes all nine possible pairs.

Question 6

From the information provided, create the sample space of possible outcomes.
-Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%. 
A) NR NNR NNR
B) NNR NNN
C) NNN RNN NR
D) N NN NR NNN NRN

Accepted Answer

The answer of From the information provided, create the sample...

Question 7

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-If you drew one card from a standard deck, would it be unlikely to draw a 5?
A) Yes
B) No

Accepted Answer

There are 4 fives in a standard deck of 52 cards, so the probability of drawing a 5 is 4/52, which simplifies to approximately 0.077. Since 0.077 is greater than 0.05, it is not considered unlikely.

Question 8

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-Assume that one student in your class of 28 students is randomly selected to win a prize. Would it be unlikely for you to win?
A) Yes
B) No

Accepted Answer

The probability of any one student winning is 1/28, which is less than or equal to 0.05. Therefore, it is unlikely for any individual student to win.

Question 9

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-Assume that a study of 500 randomly selected school bus routes showed that 482 arrived on time. Is it unlikely for a school bus to arrive late?
A) Yes
B) No

Accepted Answer

The probability of a school bus arriving late based on the given data is (500-482)/500 = 0.036, which is less than or equal to 0.05. Therefore, it is unlikely for a school bus to arrive late.

Question 10

Find the indicated probability.
-Refer to the table which summarizes the results of testing for a certain disease.  If one of the results is randomly selected, what is the probability that it is a false positive (test indicates the person has the disease when in fact they don't)? What does this probability suggest about the accuracy of the
Test?
A) 0.155; The probability of this error is high so the test is not very accurate.
B) 0.414; The probability of this error is high so the test is not very accurate.
C) 0.0256; The probability of this error is low so the test is fairly accurate.
D) 0.103; The probability of this error is high so the test is not very accurate.

Accepted Answer

The answer of Find the indicated probability.
-Refer to the table...

Question 11

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

Accepted Answer

The probability of getting a 12 when a pair of dice is rolled is 1/36, which is less than 0.05. Therefore, it is considered an unlikely event.

Question 12

Find the indicated probability.
-Refer to the table which summarizes the results of testing for a certain disease. $$\begin{array} { l | c c } 
& \text { Positive Test Result } & \text { Negative Test Result } \
\hline \text { Subject has the disease } & 111 & 4 \
\text { Subject does not have the disease } & 11 & 172
\end{array}$$ 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) 0.0134; The probability of this error is low so the test is fairly accurate.
B) 0.591; The probability of this error is high so the test is not very accurate.
C) 0.0369; The probability of this error is low so the test is fairly accurate.
D) 0.0348; The probability of this error is low so the test is fairly accurate.

Accepted Answer

The answer of Find the indicated probability.
-Refer to the table...

Question 13

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-A multiple choice question has 18 possible answers, only one of which is correct. Is it unlikely to answer a question correctly if a random guess is made?
A) Yes
B) No

Accepted Answer

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

Question 14

Find the indicated probability.
-In a certain class of students, there are 11 boys from Wilmette, 4 girls from Winnetka, 7 girls from Wilmette, 4 boys from Glencoe, 5 boys from Winnetka and 4 girls from Glencoe. If the teacher calls upon a student to
Answer a question, what is the probability that the student will be a boy?
A) 0.314
B) 0.71
C) 0.429
D) 0.571

Accepted Answer

The total number of boys = 11 + 4 + 5 = 20
The total number of students = 11 + 4 + 7 + 4 + 5 + 4 = 35
Therefore, the probability that the student will be a boy = 20/35 = 0.571.

Question 15

From the information provided, create the sample space of possible outcomes.
-Flip a coin twice.
A) HT TH
B) HH TT HT HT
C) HH HT TT
D) HH HT TH TT

Accepted Answer

The sample space for flipping a coin twice includes all possible combinations of heads (H) and tails (T), which are: HH, HT, TH, and TT.

Question 16

From the information provided, create the sample space of possible outcomes.
-Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive.
Assume that neither the white nor the black gene dominates. List the possible outcomes.
A) WW, WW
B) WB, BW
C) WW, BB
D) WW, BW

Accepted Answer

The male mouse can pass either a white (W) or black (B) gene, while the female can only pass a white (W) gene. The possible combinations are WW (white from both parents) and BW (white from the female and black from the male).

Question 17

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-Assume that a study of 300 randomly selected school bus routes showed that 274 arrived on time. Is it unlikely for a school bus to arrive late?
A) Yes
B) No

Accepted Answer

The probability of a bus arriving late is (300 - 274) / 300 = 0.0867, which is greater than 0.05, so it is not considered unlikely.

Question 18

Estimate the probability of the event.
-Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.
A) 0.29
B) 0.373
C) 0.241
D) 0.322

Accepted Answer

We can estimate the probability by taking the ratio of the number of people with high blood pressure to the total number of people who came to give blood:

P(high blood pressure) = 397/1232 ≈ 0.322

Therefore, the answer is D.

Question 19

Answer the question, considering an event to be "unlikely" 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 unlikely to guess the date of his birth (not including the year)?
A) Yes
B) No

Accepted Answer

There are typically 28 to 31 days in a month, so the probability of guessing the correct date is 1/28 to 1/31, which is less than 0.05, making it unlikely.

Question 20

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05.
-If you are told that a mystery person's name begins with a consonant, would it be unlikely to guess the first letter of that person's name?
A) Yes
B) No

Accepted Answer

There are 21 consonants in the English alphabet, out of a total of 26 letters. Therefore, the probability of guessing a consonant as the first letter of a mystery person's name is 21/26, which is greater than 0.05. As the probability is greater than 0.05, it is not considered unlikely to guess the first letter of that person's name.

Quiz 4: Probability

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. -Is it unlikely to get 11 when a pair of dice is rolled?

From the information provided, create the sample space of possible outcomes. -Flip a coin three times.

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

From the information provided, create the sample space of possible outcomes. -Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?

From the information provided, create the sample space of possible outcomes. -Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.

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

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. -Assume that one student in your class of 28 students is randomly selected to win a prize. Would it be unlikely for you to win?

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. -Assume that a study of 500 randomly selected school bus routes showed that 482 arrived on time. Is it unlikely for a school bus to arrive late?

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

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

From the information provided, create the sample space of possible outcomes. -Flip a coin twice.

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. -Assume that a study of 300 randomly selected school bus routes showed that 274 arrived on time. Is it unlikely for a school bus to arrive late?

Estimate the probability of the event. -Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

Answer the question, considering an event to be "unlikely" 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 unlikely to guess the date of his birth (not including the year) ?

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. -If you are told that a mystery person's name begins with a consonant, would it be unlikely to guess the first letter of that person's name?