Question 1

Provide an appropriate response.
-When a balanced die is rolled, the probability that a six will appear is $\frac { 1 } { 6 } .$ . Suppose that you have just rolled the die five times without getting a six. What is the probability that you will get a six on
The next roll of the die?

Accepted Answer

A)  1
B)  Greater than  16\frac { 1 } { 6 }61​  but less than 1
C)    16\frac { 1 } { 6 }61​ 
D)  0  C

Question 2

Solve the problem.
-Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards.

Accepted Answer

A)  12 to 1
B)  13 to 1
C)  1 to 12
D)  1 to 13 C

Question 3

Solve the problem.
-There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they Will guess correctly?

Accepted Answer

A)    1210\frac { 1 } { 210 }2101​ 
B)    1343\frac { 1 } { 343 }3431​ 
C)    135\frac { 1 } { 35 }351​ 
D)    121\frac { 1 } { 21 }211​ C

Question 4

Solve the problem.
-How many different five-card hands can be dealt from a deck that has only clubs (13 cards altogether)?

Accepted Answer

A)  143
B)  1,287
C)  2,574
D)  3,861

Question 5

Determine whether the events A and B are independent.
-Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others. 
Event A: The first person does not pick the short straw
Event B: The second person picks the short straw

Accepted Answer

A) True 
 B)False

Question 6

Provide an appropriate response.
-Event A is that Lisa votes for Candidate A in the gubernatorial election and event B is that she votes for candidate B. Are events A and B: A: Overlapping, Independent?
B: Overlapping, Dependent?
$\mathrm { C } :$ Non-overlapping, Independent?
D: Non-overlapping, Dependent?

Accepted Answer

A)  B
B)  D
C)  A
D)  C

Question 7

Find the expected value.
-You are given 12 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn).
This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to
You)of the game. Round to the nearest cent.

Accepted Answer

A)  -$0.19
B)  $0.19
C)  -$0.92
D)  $2.25

Question 8

Make a probability distribution for the given set of events.
-When two fair dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$
$( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$
$( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$
$( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$
$( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$
$( 6,1 ) \quad ( 6,2 ) \quad ( 6,3 ) \quad( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Find the probability distribution for the product of the two numbers that appear when two fair dice are rolled.

Accepted Answer

A)    Product  Probability 11/1821/1831/1841/1851/1861/1881/1891/18101/18\begin{array}{r|r}	ext { Product } & 	ext { Probability } \\hline 1 & 1 / 18 \2 & 1 / 18 \3 & 1 / 18 \4 & 1 / 18 \5 & 1 / 18 \6 & 1 / 18 \8 & 1 / 18 \9 & 1 / 18 \10 & 1 / 18\end{array} Product 1234568910​ Probability 1/181/181/181/181/181/181/181/181/18​​   Product  Probability 121/18151/18161/18181/18201/18241/18251/18301/18361/18\begin{array}{r|r}	ext { Product } & 	ext { Probability } \\hline 12 & 1 / 18 \15 & 1 / 18 \16 & 1 / 18 \18 & 1 / 18 \20 & 1 / 18 \24 & 1 / 18 \25 & 1 / 18 \30 & 1 / 18 \36 & 1 / 18\end{array} Product 121516182024253036​ Probability 1/181/181/181/181/181/181/181/181/18​​ 
B)    Product  Probability 21/3631/1841/1251/965/36\begin{array}{r|r}	ext { Product } & 	ext { Probability } \\hline 2 & 1 / 36 \3 & 1 / 18 \4 & 1 / 12 \5 & 1 / 9 \6 & 5 / 36\end{array} Product 23456​ Probability 1/361/181/121/95/36​​   Product  Probability 71/685/3691/9101/12111/18121/36\begin{array}{r|r}	ext { Product } & 	ext { Probability } \\hline 7 & 1 / 6 \8 & 5 / 36 \9 & 1 / 9 \10 & 1 / 12 \11 & 1 / 18 \12 & 1 / 36\end{array} Product 789101112​ Probability 1/65/361/91/121/181/36​​ 
C)    Product  Probability 21/1831/1841/1251/1861/981/18\begin{array}{r|r}	ext { Product } & 	ext { Probability } \\hline 2 & 1 / 18 \3 & 1 / 18 \4 & 1 / 12 \5 & 1 / 18 \6 & 1 / 9 \8 & 1 / 18\end{array} Product 234568​ Probability 1/181/181/121/181/91/18​​   Product|  Probability 101/12121/9151/12181/12201/12241/12301/18\begin{array}{r|r}	ext { Product| } & 	ext { Probability } \\hline 10 & 1 / 12 \12 & 1 / 9 \15 & 1 / 12 \18 & 1 / 12 \20 & 1 / 12 \24 & 1 / 12 \30 & 1 / 18\end{array} Product| 10121518202430​ Probability 1/121/91/121/121/121/121/18​​ 
D)     Product  Probability  Product  Probability 11/36121/921/18151/1831/18161/3641/12181/1851/18201/1861/9241/1881/18251/3691/36301/18101/18361/36\begin{array}{l}\begin{array} { r | r r | r } 	ext { Product } & 	ext { Probability } & 	ext { Product } & 	ext { Probability } \\hline 1 & 1 / 36 & 12 & 1 / 9 \2 & 1 / 18 & 15 & 1 / 18 \3 & 1 / 18 & 16 & 1 / 36 \4 & 1 / 12 & 18 & 1 / 18 \5 & 1 / 18 & 20 & 1 / 18 \6 & 1 / 9 & 24 & 1 / 18 \8 & 1 / 18 & 25 & 1 / 36 \9 & 1 / 36 & 30 & 1 / 18 \10 & 1 / 18 & 36 & 1 / 36\end{array}\end{array} Product 1234568910​ Probability 1/361/181/181/121/181/91/181/361/18​ Product 121516182024253036​ Probability 1/91/181/361/181/181/181/361/181/36​​​

Question 9

Solve the problem. Round your answer to 2 decimal places when necessary.
-The overall U.S. death rate for 60 year-olds is approximately 12 deaths per 1000 people. Suppose that a life insurance company insures 2000 60-year-old people. The cost of the premium is $760 per
Year, and the death benefit is $60,000. What is the expected profit or loss for the insurance
Company?

Accepted Answer

A)  $61,760 profit
B)  $200,000 profit
C)  $80,000 profit
D)  $1,440,000 loss

Question 10

Solve the problem.
-A student is told to answer any 7 out of 10 questions on an exam. In how many different ways can he choose the 7 questions to answer?

Accepted Answer

A)  720
B)  120
C)  21
D)  10,000,000

Question 11

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Accepted Answer

A)   3
B)    518\frac { 5 } { 18 }185​ 
C)    118\frac { 1 } { 18 }181​ 
D)    112\frac { 1 } { 12 }121​

Question 12

Evaluate the factorial expression.
-$\frac { 10 ! } { 9 ! }$

Accepted Answer

A)   1
B)   10 !
C)   10
D)    109\frac { 10 } { 9 }910​

Question 13

Write the word or phrase that best completes each statement or answers the question.
-Suppose a mathematician computed the expected winnings (to the player)of each of seven
different games in a casino. What would you expect to be true for all expected winnings?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Decide whether events A and B are overlapping or non-overlapping.
-A person is selected at random from a group of doctors. Event A is that the person selected is a woman. Event B is that the person selected is a surgeon.

Accepted Answer

A)  Overlapping
B)  Non-overlapping

Question 15

Decide whether events A and B are overlapping or non-overlapping.
-You roll a red die and a blue die. Event A is that you get a sum of 9.
Event B is that you get a sum of 3.

Accepted Answer

A)  Overlapping
B)  Non-overlapping

Question 16

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?

Accepted Answer

A)    219\frac { 2 } { 19 }192​ 
B)    919\frac { 9 } { 19 }199​ 
C)    12\frac { 1 } { 2 }21​ 
D)    199\frac { 19 } { 9 }919​

Question 17

Find the indicated probability.
-In a poll of registered voters shortly before a mayoral election, people were asked which candidate they were planning to vote for. The results are shown in the table. $$\begin{array} { c | c } 
\text { Candidate } & \text { Frequency } \
\hline \text { Ford } & 269 \
\text { Anderson } & 342 \
\text { Garcia } & 527 \
\text { Wong } & 526
\end{array}$$ Find the empirical probability that a randomly selected registered voter is planning to vote for
Anderson. Round your answer to the nearest thousandth when necessary.

Accepted Answer

A)  0.301
B)  0.206
C)  0.003
D)  342

Question 18

Find the indicated probability.
-The following table show the results of a clinical trial for an allergy drug. $$\begin{array} { l | c | c | c | c } 
& \begin{array} { c } 
\text { Allergy } \
\text { drug }
\end{array} & \text { Placebo } & \begin{array} { c } 
\text { Control } \
\text { (no treatment) }
\end{array} & \text { Total } \
\hline \text { Improvement } & 145 & 85 & 41 & 271 \
\text { No improvement } & 55 & 115 & 59 & 229 \
\text { Total } & 200 & 200 & 100 & 500
\end{array}$$ What is the probability that a randomly selected person either was given the allergy drug or did not improve? Round your answer to the nearest thousandth when necessary.

Accepted Answer

A)  0.858
B)  0.748
C)  0.11
D)  0.458

Question 19

Use the at least once rule to find the indicated probability.
-The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

Accepted Answer

A)  0.975
B)  0.001
C)  0.025
D)  0.960

Question 20

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Accepted Answer

A)    112\frac { 1 } { 12 }121​ 
B)    56\frac { 5 } { 6 }65​ 
C)    1112\frac { 11 } { 12 }1211​ 
D)   10

Exam 7: Probability: Living With the Odds

Provide an appropriate response. -When a balanced die is rolled, the probability that a six will appear is $\frac { 1 } { 6 } .$ . Suppose that you have just rolled the die five times without getting a six. What is the probability that you will get a six on The next roll of the die?

Solve the problem. -Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards.

Solve the problem. -There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order) , what is the probability that they Will guess correctly?

Solve the problem. -How many different five-card hands can be dealt from a deck that has only clubs (13 cards altogether) ?

Determine whether the events A and B are independent. -Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others. Event A: The first person does not pick the short straw Event B: The second person picks the short straw

Solve the problem. -A student is told to answer any 7 out of 10 questions on an exam. In how many different ways can he choose the 7 questions to answer?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Evaluate the factorial expression. - $\frac { 10 ! } { 9 ! }$

Write the word or phrase that best completes each statement or answers the question. -Suppose a mathematician computed the expected winnings (to the player)of each of seven different games in a casino. What would you expect to be true for all expected winnings?

Decide whether events A and B are overlapping or non-overlapping. -A person is selected at random from a group of doctors. Event A is that the person selected is a woman. Event B is that the person selected is a surgeon.

Decide whether events A and B are overlapping or non-overlapping. -You roll a red die and a blue die. Event A is that you get a sum of 9. Event B is that you get a sum of 3.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?

Use the at least once rule to find the indicated probability. -The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A die with 12 sides is rolled. What is the probability of rolling a number less than 11?