Question 1

From the information provided, create the sample space of possible outcomes
-In a certain class of students, there are 12 boys from Wilmette, 3 girls from Winnetka, 8 girls from Wilmette, 4 boys from Glencoe, 3 boys from Winnetka and 9 girls from Glenoce. If the teacher calls upon a student to answer a question, what is the probability that the student will be a boy?
A)0.308
B)0.487
C)0.767
D)0.41

Accepted Answer

The total number of students is 12 boys from Wilmette + 3 girls from Winnetka + 8 girls from Wilmette + 4 boys from Glencoe + 3 boys from Winnetka + 9 girls from Glencoe = 39 students. The total number of boys is 12 (Wilmette) + 4 (Glencoe) + 3 (Winnetka) = 19 boys. Therefore, the probability of selecting a boy is 19/39 = 0.487.

Question 2

Find the indicated probability
-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

Estimate the probability of the event
-In a certain class of students, there are 9 boys from Wilmette, 5 girls from Kenilworth, 7 girls from Wilmette, 6 boys from Glencoe, 5 boys from Kenilworth and 3 girls from Glenoce. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?
A)0.25
B)0.37
C)0.286
D)0.143

Accepted Answer

There are a total of 35 students (9 boys from Wilmette + 5 girls from Kenilworth + 7 girls from Wilmette + 6 boys from Glencoe + 5 boys from Kenilworth + 3 girls from Glencoe). The number of students from Kenilworth is 10 (5 girls + 5 boys). The probability is 10/35 = 0.286.

Question 4

Estimate the probability of the event
-Assume that one student in your class of 31 students is randomly selected to win a prize. Would it be "unusual" for you to win?
A)No
B)Yes

Accepted Answer

The probability of winning is 1/31, which is approximately 0.0323 or 3.23%. This is a low probability, making it unusual for any specific student, including you, to win.

Question 5

Estimate the probability of the event
-Of 1338 people who came into a blood bank to give blood, 253 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.
A)0.157
B)0.189
C)0.24
D)0.108

Accepted Answer

The probability can be estimated by dividing the number of people with high blood pressure by the total number of people who came in. So, it's 253/1338 = 0.189.

Question 6

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)NNR NNN
B)N NN NR NNN NRN
C)NNN RNN NR
D)NR NNR NNR

Accepted Answer

The correct answer is A because it is the only option that has three normal pups and two runts.

Question 7

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-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD
B) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD
C) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP
D) CD-LD LD-LP LP-CD LP-LP LD-LD

Accepted Answer

Each person has the same set of candies (lemon drop, cherry drop, lollipop), so any combination of candies eaten by Fred and Ed is possible, including eating the same type of candy. Option B lists all unique combinations, including those where they eat the same candy and those where they eat different candies.

Question 8

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 TH TT
D)HH HT TT

Accepted Answer

When flipping a coin twice, the sample space consists of all possible outcomes: HH (heads first, then heads), HT (heads, then tails), TH (tails, then heads), and TT (tails, then tails).

Question 9

Find the indicated probability
-Is it "unusual" to get a 12 when a pair of dice is rolled?
A)No
B)Yes

Accepted Answer

When rolling a pair of six-sided dice, the probability of getting a sum of 12 is 1/36, as there is only one combination (6,6) that results in a 12. This is a low probability event, making it unusual.

Question 10

Find the indicated probability
-If you drew one card from a standard deck, would it be "unusual" to draw an ace of hearts?
A)Yes
B)No

Accepted Answer

Drawing an ace of hearts from a standard deck of 52 cards has a probability of 1/52, which is considered unusual because it is a low probability event.

Question 11

Find the indicated probability
-Assume that a study of 500 randomly selected school bus routes showed that 486 arrived on time. Is it "unusual" for a school bus to arrive late?
A)No
B)Yes

Accepted Answer

The answer of Find the indicated probability
-Assume that a study...

Question 12

Find the indicated probability
-If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's name?
A)Yes
B)No

Accepted Answer

The answer of Find the indicated probability
-If you are told...

Question 13

Find the indicated probability
-Is it "unusual" to get 9 when a pair of dice is rolled?
A)Yes
B)No

Accepted Answer

The probability of rolling a sum of 9 with two dice is 4 out of 36 (or 1 out of 9) since there are four combinations (3,6), (4,5), (5,4), and (6,3) that result in a sum of 9. This probability does not qualify as "unusual," which is typically considered to be events with a probability of less than 5%.

Question 14

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)0.65
B)0.6
C)0.4
D)0.5

Accepted Answer

The probability of the referendum passing is the proportion of '0's in the data set. There are 12 '0's out of 20 responses, so the probability is 12/20 = 0.6.

Question 15

Find the indicated probability
-If you drew one card from a standard deck, would it be "unusual" to draw a 7?
A)Yes
B)No

Accepted Answer

Drawing a 7 from a standard deck of cards is not unusual because there are 4 sevens in a deck of 52 cards, making the probability of drawing a 7 about 1 in 13, which is a fairly common outcome.

Question 16

Find the indicated probability
-A multiple choice question has 16 possible answers, only one of which is correct. Is it "unusual" to answer a question correctly if a random guess is made?
A)No
B)Yes

Accepted Answer

With 16 possible answers and only one correct answer, the probability of guessing correctly is 1/16 or 6.25%, which is low but not considered "unusual" in the context of random guessing on a multiple-choice question.

Question 17

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

Accepted Answer

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

Question 18

Find the indicated probability
-In a poll, respondents were asked whether they had ever been in a car accident. 196 respondents indicated that they had been in a car accident and 118 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)0.376
B)0.624
C)0.005
D)1.661

Accepted Answer

The probability is calculated by dividing the number of respondents who have been in a car accident by the total number of respondents. So, it's 196 / (196 + 118) = 196 / 314 = 0.624.

Question 19

Estimate the probability of the event
-The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $90,000. Round your answers to the nearest tenth. $$\begin{array} { l } 
104,000118,00084,000125,00087,000104,00090,00078,000139,000174,00081,00097,000132,00087,000118,000 \
111,00090,000146,00075,000111,000
\end{array}$$
A)0.4
B)0.7
C)0.8
D)0.6

Accepted Answer

To estimate the probability that a randomly selected member earns at least $90,000, count the number of members earning $90,000 or more and divide by the total number of members. There are 14 members earning at least $90,000 out of 20 members total, so the probability is 14/20 = 0.7.

Question 20

Find the indicated probability
-Assume that a study of 300 randomly selected school bus routes showed that 272 arrived on time. Is it "unusual" for a school bus to arrive late?
A)Yes
B)No

Accepted Answer

The probability of a school bus arriving late is 1 - 272/300 = 0.093. This is not an unusual event, as it is greater than 0.05.

Quiz 4: Probability

Find the indicated probability -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) ?

Estimate the probability of the event -Assume that one student in your class of 31 students is randomly selected to win a prize. Would it be "unusual" for you to win?

Estimate the probability of the event -Of 1338 people who came into a blood bank to give blood, 253 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

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%.

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 -Flip a coin twice.

Find the indicated probability -Is it "unusual" to get a 12 when a pair of dice is rolled?

Find the indicated probability -If you drew one card from a standard deck, would it be "unusual" to draw an ace of hearts?

Find the indicated probability -Assume that a study of 500 randomly selected school bus routes showed that 486 arrived on time. Is it "unusual" for a school bus to arrive late?

Find the indicated probability -If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's name?

Find the indicated probability -Is it "unusual" to get 9 when a pair of dice is rolled?

Find the indicated probability -If you drew one card from a standard deck, would it be "unusual" to draw a 7?

Find the indicated probability -A multiple choice question has 16 possible answers, only one of which is correct. Is it "unusual" 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 three times.

Find the indicated probability -Assume that a study of 300 randomly selected school bus routes showed that 272 arrived on time. Is it "unusual" for a school bus to arrive late?