Question 1

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. What is the probability of getting at least one head and at least one tail?

Accepted Answer

The answer of If you flip a coin three times,...

Question 2

The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number living out of an original 100,000, and the additional life expectancy for a person of that age.
Exact Male Female P(Death Additional P(Death Additional Age 
\(\begin{array}{c}
\quad\quad\quad\text { Male }  \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Female }\
\begin{array}{|c|c|c|c|c|c|c|}
\hline{\text {Exact  Age }} & \begin{array}{c}
\text { P(Death } \
\text { within one } \
\text { year) }
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Living }
\end{array} & \begin{array}{c}
\text { Additional } \
\text { Life } \
\text { Expectancy }
\end{array} & \begin{array}{c}
\text { P(Death } \
\text { within one } \
\text { year) }
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Living }
\end{array} & \begin{array}{c}
\text { Additional } \
\text { Life } \
\text { Expectancy }
\end{array} \
\hline 10 & 0.000111 & 99,021 & 65.13 & 0.000105 & 99,217 & 70.22 \
\hline 20 & 0.001287 & 98,451 & 55.46 & 0.000469 & 98,950 & 60.40 \
\hline 30 & 0.001375 & 97,113 & 46.16 & 0.000627 & 98,431 & 50.69 \
\hline 40 & 0.002542 & 95,427 & 36.88 & 0.001498 & 97,513 & 41.11 \
\hline 50 & 0.005696 & 91,853 & 28.09 & 0.003240 & 95,378 & 31.91 \
\hline 60 & 0.012263 & 84,692 & 20.00 & 0.007740 & 90,847 & 23.21 \
\hline 70 & 0.028904 & 70,214 & 12.98 & 0.018938 & 80,583 & 15.45 \
\hline 80 & 0.071687 & 44,272 & 7.43 & 0.049527 & 59,341 & 9.00 \
\hline 90 & 0.188644 & 12,868 & 3.68 & 0.146696 & 24,331 & 4.45 \
\hline
\end{array}\end{array}\) 
To what age may a male of age 60 expect to live on the average?

Accepted Answer

The answer of The following table is from the Social...

Question 3

From four men and two women, a committee is formed by drawing four names out of a hat.
List all possible drawings and determine the probability that two men and two women are selected. (Hint: Your list should contain 15 possibilities.)

Accepted Answer

The answer of From four men and two women, a...

Question 4

The advertising for a cold remedy claimed that no other cold remedy acted faster. In a experiment to compare that remedy with another one, it did act faster on average, but the result was not significant. What does this mean?
A) The difference was so small that it could have happened by chance even if the remedies were equivalent.
B) The difference was so small that it could have happened by chance even if the remedies were not equivalent.
C) The probability of the observed difference occurring by chance if the two remedies are equivalent was less than 0.05.
D) The population mean response times are different, but the samples didn't show it.

Accepted Answer

The result not being significant means that the observed difference could have occurred by chance, suggesting no strong evidence that the remedies are different in effectiveness.

Question 5

A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (Hint: There are 16 possible outcomes.)

Accepted Answer

The answer of A bag contains four chips of which...

Question 6

If a sample space has 5000 equally likely possible outcomes, what is the probability of each one?

Accepted Answer

The answer of If a sample space has 5000 equally...

Question 7

state whether there is one way for the given observation to occur (outcome) or more than one way for the observation to occur (event).
-Five electronic switches are tested at random from a day's production and the first one is found to be defective. Not knowing the status of the other four, is this observation an outcome or an event?
A) Outcome
B) Event

Accepted Answer

This is an event because there are multiple ways the first switch can be defective while the status of the other four remains unknown.

Question 8

Is it significant to be dealt an ace when you are dealt one card from a standard 52-card deck.
(There are four aces in the deck.)

Accepted Answer

The answer of Is it significant to be dealt an...

Question 9

From the table in Problem 16, how many 50-year old females on average will be living at age 51?

Accepted Answer

The answer of From the table in Problem 16, how...

Question 10

If a person is randomly selected, find the probability that his or her birthday is not in May.
Ignore leap years. There are 365 days in a year. Express your answer as a fraction.

Accepted Answer

The answer of If a person is randomly selected, find...

Question 11

In a certain class of students, there are 10 boys from Wilmette, 4 girls from Kenilworth, 9 girls from Wilmette, 5 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe.
If the teacher calls upon a student to answer a question, what is the probability that the student will be a girl? Express your answer to 3 decimal places.

Accepted Answer

The answer of In a certain class of students, there...

Question 12

A bag of marbles hold 5 red marbles, 6 green marbles and 14 blue marbles. If one marble is drawn out, what is the probability that it green?

Accepted Answer

The answer of A bag of marbles hold 5 red...

Question 13

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.
A) The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.
B) The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.
C) The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.
D) The series closest to the theoretical 50/50 cannot be determined without knowing the
Number of odds and evens in each series.

Accepted Answer

The Tuesday series has 13 odd and 5 even (13/18), which is closer to 0.5 than Monday's 9 odd and 3 even (9/12).

Question 14

100 employees of a company are asked how they get to work and whether they work full time or part time. The following figure shows the results for transportation. If one of the 100 employees is randomly selected, find the probability that the person does not ride a bicycle.  
A) Public transportation: 8 full time, 9 part time
B) Bicycle: 3 full time, 5 part time
C) Drive alone: 29 full time, 27 part time
D) Carpool: 9 full time, 10 part time

Accepted Answer

The answer of 100 employees of a company are asked...

Question 15

A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man's expected value for the insurance policy?
A) $139,916
B) ?$41
C) $84
D) ?$124

Accepted Answer

The answer of A 28-year-old man pays $125 for a...

Question 16

state whether there is one way for the given observation to occur (outcome) or more than one way for the observation to occur (event).
-A coin is tossed three times and HHT (heads, heads, tails) is observed. Is this result an outcome or an event?
A) Outcome
B) Event

Accepted Answer

HHT is a specific sequence of outcomes, so it is an outcome.

Question 17

In a poll, respondents were asked whether they had ever been in a car accident. 
respondents indicated that they had been in a car accident and 370 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.

Accepted Answer

The answer of In a poll, respondents were asked whether...

Question 18

A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain.

Accepted Answer

The answer of A die with 12 sides is rolled....

Question 19

A collection of western novels by Zane Grey available from Amazon for a Kindle device contains 26 novels. If one novel is selected at random, would it be considered significant if the novel selected was The Mysterious Rider.

Accepted Answer

The question states that there are 26 novels in the collection. If one novel is selected at random, then each novel has an equal chance of being selected. Therefore, the probability of selecting The Mysterious Rider is 1/26, which is approximately 3.8%. This is not considered to be a significant probability, so it would not be considered significant if The Mysterious Rider was selected.

Question 20

Suppose you have an extremely unfair coin: The probability of a head is 1/5, and the probability of a tail is 4/5 . If you toss the coin 40 times, how many heads do you expect to see?

Accepted Answer

The answer of Suppose you have an extremely unfair coin:...

Quiz 6: Probability in Statistics

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. What is the probability of getting at least one head and at least one tail?

From four men and two women, a committee is formed by drawing four names out of a hat. List all possible drawings and determine the probability that two men and two women are selected. (Hint: Your list should contain 15 possibilities.)

The advertising for a cold remedy claimed that no other cold remedy acted faster. In a experiment to compare that remedy with another one, it did act faster on average, but the result was not significant. What does this mean?

If a sample space has 5000 equally likely possible outcomes, what is the probability of each one?

Is it significant to be dealt an ace when you are dealt one card from a standard 52-card deck. (There are four aces in the deck.)

From the table in Problem 16, how many 50-year old females on average will be living at age 51?

If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. There are 365 days in a year. Express your answer as a fraction.

A bag of marbles hold 5 red marbles, 6 green marbles and 14 blue marbles. If one marble is drawn out, what is the probability that it green?

A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man's expected value for the insurance policy?

state whether there is one way for the given observation to occur (outcome) or more than one way for the observation to occur (event) . -A coin is tossed three times and HHT (heads, heads, tails) is observed. Is this result an outcome or an event?

A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain.

A collection of western novels by Zane Grey available from Amazon for a Kindle device contains 26 novels. If one novel is selected at random, would it be considered significant if the novel selected was The Mysterious Rider.

Suppose you have an extremely unfair coin: The probability of a head is 1/5, and the probability of a tail is 4/5 . If you toss the coin 40 times, how many heads do you expect to see?