Question 1

An oil-drilling company knows that it costs $65,000 to sink a test well. If oil is hit, the income for the drilling company will be $550,000. If only natural gas is hit, the income will be $428,373. If nothing is hit, there will be no income. If the probability of hitting oil is 1/65 and if the probability of hitting gas is 1/35, what is the expectation for the drilling company? Should the company sink the test well? ​
A) - $55,216; should dig
B) $44,299; should dig
C) - $44,299; should dig
D) - $44,299; should not dig
E) - $42,695; should not dig

Accepted Answer

The expectation (E) can be calculated using the formula: E = (P(oil) * Income(oil)) + (P(gas) * Income(gas)) + (P(nothing) * Income(nothing)) - Cost. Here, P(oil) = 1/65, Income(oil) = $550,000; P(gas) = 1/35, Income(gas) = $428,373; Income(nothing) = $0; Cost = $65,000. The probability of hitting nothing is 1 - P(oil) - P(gas). Calculating E gives a negative value, indicating a loss, hence the company should not dig.

Question 2

What is the expectation for the $1 five-number bet on a U.S. roulette wheel?
​  ​
$__________

Accepted Answer

The answer of What is the expectation for the $1...

Question 3

A box contains one each of $2, $8, $40, $65, and $100 bills. You reach in and withdraw one bill. What is the expected value? Please round your answer to the nearest dollar.
​
$__________

Accepted Answer

The answer of A box contains one each of $2,...

Question 4

Use estimation to find the expected value. Do not calculate.
​
The expected value of playing a $1 game of blackjack is $0.04, find the netted value after playing the game 100 times.
​
The netted value is $__________.

Accepted Answer

The answer of Use estimation to find the expected value....

Question 5

A box contains one each of $4, $8, $25, $90, and $100 bills. You reach in and withdraw one bill. What is the expected value? ​
A) $114
B) $45
C) $25
D) $20
E) $227

Accepted Answer

The expected value is calculated by adding all the values together and then dividing by the number of values. So, ($4 + $8 + $25 + $90 + $100) / 5 = $227 / 5 = $45.

Question 6

In a TV game show, four prizes are hidden on a game board which contains 60 spaces. One prize is worth $1,500, two prizes are worth $750, and the other prize is worth $50. The remaining spaces contain no prizes. The game show host offers a sure prize of $50 not to play this game. Should the contestant choose the sure prize or play the game?
​
Answer play, doesn't matter, or don't play.

Accepted Answer

The answer of In a TV game show, four prizes...

Question 7

Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling the dice? Please round your answer to the nearest cent.
​
$__________

Accepted Answer

The answer of Suppose that you roll two dice. You...

Question 8

Heights (in inches) obtained by a group of people in a random survey is reported in the table. What is the expected height (in inches)? Heights
Probability
55
0)007
60
0)024
65
0)112
70
0)357
75
0)357
80
0)112
85
0)024
90
0)007
​
A) 80 in.
B) 78.3 in.
C) 78 in.
D) 71.8 in.
E) 72.5 in.

Accepted Answer

The answer of Heights (in inches) obtained by a group...

Question 9

In a TV game show, four prizes are hidden on a game board which contains 80 spaces. One prize is worth $4,000, two prizes are worth $2,000, and the other prize is worth $100. The remaining spaces contain no prizes. The game show host offers a sure prize of $100 not to play this game. Should the contestant choose the sure prize or play the game? ​
A) doesn't matter
B) play
C) don't play

Accepted Answer

There are 4 total prizes worth a total of $8,100. There are 76 blank spaces on the game board. Therefore, the probability of winning any prize is 4/80 or 1/20.

The expected value of playing the game can be calculated as:
(1/20 x $4000) + (2/20 x $2000) + (1/20 x $100) = $500

This means that, on average, a contestant can expect to win $500 by playing the game. Therefore, it would be more advantageous for the contestant to play the game and try to win one of the prizes rather than accepting the sure prize of $100.

Question 10

What is the expectation for the $1 four-number bet on a U.S. roulette wheel? ​  ​
A) $0.05
B) $0.08
C) - $0.01
D) - $0.08
E) - $0.05

Accepted Answer

The answer of What is the expectation for the $1...

Question 11

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from four hidden windows. Behind each is one of the following: $250,000, $125,000, $1 million, or a "stopper." Before beginning, the contestant is offered $300,000 to stop. Mathematically speaking, should the contestant take the $300,000?
​
Answer yes, no, or doesn't matter.

Accepted Answer

The answer of Consider a state lottery that has a...

Question 12

What is the expectation for the $1 black bet on a U.S. roulette wheel?
​  ​
$__________

Accepted Answer

The answer of What is the expectation for the $1...

Question 13

Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is $70,000; 7 second prizes each pay $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there are 6 million entries? Please round your answer to the nearest cent.
​
$__________

Accepted Answer

The answer of Krinkles potato chips is having a "Lucky...

Question 14

What is the expectation for the $1 black bet on a U.S. roulette wheel? ​  ​
A) $0.05
B) - $0.01
C) $0.02
D) - $0.08
E) - $0.05

Accepted Answer

The answer of What is the expectation for the $1...

Question 15

Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is $70,000; 7 second prizes each pay $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there are 9 million entries? ​
A) $0.05
B) $0.86
C) $0.03
D) $0.25
E) $0.01

Accepted Answer

The answer of Krinkles potato chips is having a "Lucky...

Question 16

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability. ​  ​  ​
A) 
B) ​ 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of A single card is selected from an...

Question 17

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from four hidden windows. Behind each is one of the following: $225,000, $300,000, $1 million, or a "stopper." Before beginning, the contestant is offered $400,000 to stop. Mathematically speaking, should the contestant take the $400,000? ​
A) yes
B) I don't know
C) doesn't matter
D) no

Accepted Answer

The expected value of playing is calculated by averaging the possible outcomes: (225,000 + 300,000 + 1,000,000 + 0) / 4 = $381,250. Since $400,000 is greater than the expected value of $381,250, the contestant should take the $400,000 offer.

Question 18

Last year, 1,303 calculators were returned to the manufacturer. If 81,000 were produced, assign a number to specify the probability that a particular calculator would be returned. ​
A) about 0.016
B) about 0.130
C) about 0.033
D) about 0.058
E) about 0.012

Accepted Answer

The probability is calculated by dividing the number of calculators returned (1,303) by the total produced (81,000), which gives approximately 0.016.

Question 19

An oil-drilling company knows that it costs $95,000 to sink a test well. If oil is hit, the income for the drilling company will be $875,000. If only natural gas is hit, the income will be $340,648. If nothing is hit, there will be no income. If the probability of hitting oil is  and if the probability of hitting gas is  , what is the expectation for the drilling company? Should the company sink the test well? Please round your answer to the nearest dollar.
​
The expectation is __________, the company __________ (should, shouldn't) dig.

Accepted Answer

The answer of An oil-drilling company knows that it costs...

Question 20

For the spinners assume that the pointer can never lie on a border line. Find  . ​  ​
A)  
B) ​  
C) ​  
D) ​  
E) ​

Accepted Answer

The answer of For the spinners assume that the pointer...

Quiz 13: The Nature of Probability

What is the expectation for the $1 five-number bet on a U.S. roulette wheel? $__________

A box contains one each of $2, $8, $40, $65, and $100 bills. You reach in and withdraw one bill. What is the expected value? Please round your answer to the nearest dollar. $__________

Use estimation to find the expected value. Do not calculate. The expected value of playing a $1 game of blackjack is $0.04, find the netted value after playing the game 100 times. The netted value is $__________.

A box contains one each of $4, $8, $25, $90, and $100 bills. You reach in and withdraw one bill. What is the expected value?

Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling the dice? Please round your answer to the nearest cent. $__________

Heights (in inches) obtained by a group of people in a random survey is reported in the table. What is the expected height (in inches) ? Heights Probability 55 0) 007 60 0) 024 65 0) 112 70 0) 357 75 0) 357 80 0) 112 85 0) 024 90 0) 007

What is the expectation for the $1 four-number bet on a U.S. roulette wheel?

What is the expectation for the $1 black bet on a U.S. roulette wheel? $__________

What is the expectation for the $1 black bet on a U.S. roulette wheel?

Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is $70,000; 7 second prizes each pay $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there are 9 million entries?

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability.

Last year, 1,303 calculators were returned to the manufacturer. If 81,000 were produced, assign a number to specify the probability that a particular calculator would be returned.

For the spinners assume that the pointer can never lie on a border line. Find .

Quiz 13: The Nature of Probability

What is the expectation for the $1 five-number bet on a U.S. roulette wheel? ​ ​ $__________

A box contains one each of $2, $8, $40, $65, and $100 bills. You reach in and withdraw one bill. What is the expected value? Please round your answer to the nearest dollar. ​ $__________

Use estimation to find the expected value. Do not calculate. ​ The expected value of playing a $1 game of blackjack is $0.04, find the netted value after playing the game 100 times. ​ The netted value is $__________.

A box contains one each of $4, $8, $25, $90, and $100 bills. You reach in and withdraw one bill. What is the expected value? ​

Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling the dice? Please round your answer to the nearest cent. ​ $__________

Heights (in inches) obtained by a group of people in a random survey is reported in the table. What is the expected height (in inches) ? Heights Probability 55 0) 007 60 0) 024 65 0) 112 70 0) 357 75 0) 357 80 0) 112 85 0) 024 90 0) 007 ​

What is the expectation for the $1 four-number bet on a U.S. roulette wheel? ​ ​

What is the expectation for the $1 black bet on a U.S. roulette wheel? ​ ​ $__________

What is the expectation for the $1 black bet on a U.S. roulette wheel? ​ ​

Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is $70,000; 7 second prizes each pay $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there are 9 million entries? ​

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability. ​ ​ ​

Last year, 1,303 calculators were returned to the manufacturer. If 81,000 were produced, assign a number to specify the probability that a particular calculator would be returned. ​

For the spinners assume that the pointer can never lie on a border line. Find . ​ ​

What is the expectation for the $1 five-number bet on a U.S. roulette wheel? $__________

A box contains one each of $2, $8, $40, $65, and $100 bills. You reach in and withdraw one bill. What is the expected value? Please round your answer to the nearest dollar. $__________

Use estimation to find the expected value. Do not calculate. The expected value of playing a $1 game of blackjack is $0.04, find the netted value after playing the game 100 times. The netted value is $__________.

A box contains one each of $4, $8, $25, $90, and $100 bills. You reach in and withdraw one bill. What is the expected value?

Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling the dice? Please round your answer to the nearest cent. $__________

Heights (in inches) obtained by a group of people in a random survey is reported in the table. What is the expected height (in inches) ? Heights Probability 55 0) 007 60 0) 024 65 0) 112 70 0) 357 75 0) 357 80 0) 112 85 0) 024 90 0) 007

What is the expectation for the $1 four-number bet on a U.S. roulette wheel?

What is the expectation for the $1 black bet on a U.S. roulette wheel? $__________

What is the expectation for the $1 black bet on a U.S. roulette wheel?

Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is $70,000; 7 second prizes each pay $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there are 9 million entries?

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability.

Last year, 1,303 calculators were returned to the manufacturer. If 81,000 were produced, assign a number to specify the probability that a particular calculator would be returned.

For the spinners assume that the pointer can never lie on a border line. Find .