Deck 16: Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk

Question 1

You spin the spinner shown below two separate times and record the sequence of colors. Write out the sample space. (Note: You can use G for green, B for blue, and so on.)

Answer 1

{GG,GR,GB,GY,BG,BR,BB,BY,RG,RR,RB,RY,YG,YR,YB,YY}

Question 2

On your i-pod there are a total of 150 songs. Of these 150 songs, 50 are pop, 80 are rock and the rest are rap. Suppose that you need to make a playlist consisting of 6 songs. How many different groupings of songs can you create so that there are no repeats and there are exactly three rap songs and exactly two pop songs?

Answer 2

1340640000 options

Question 3

At the local ice-cream stand a Super Sundae comes with three scoops of ice-cream. There are twenty different flavors of ice-cream available. If each scoop in the Super Sundae is a different flavor, then how many different combinations are possible?

Answer 3

1140 sundaes

Question 4

A standard deck of playing cards has two red suits (hearts and diamonds) and two black suits (spades and clubs). Each suit contains 13 cards: (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace). The 2 is the lowest valued card while the Ace is the highest valued card. Finally, the Jack, Queen, and King are called face cards. If the deck is well shuffled, then what is the probability of the following event? Give your answer as a fraction in reduced form.
E1 :"drawing a red face card or a diamond."

Question 5

Evaluate the following:

Question 6

A standard deck of playing cards has two red suits (hearts and diamonds) and two black suits (spades and clubs). Each suit contains 13 cards: (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace). The 2 is the lowest valued card while the Ace is the highest valued card. Finally, the Jack, Queen, and King are called face cards. If the deck is well shuffled, then what is the probability of the following event?
Give your answer as a fraction in reduced form.
E1 :"drawing a red card lower than a 6"

Question 7

Your college ID contains an alpha-numeric identification code which the college uses to indentify your meal plan. The code consists of five characters where the first three characters are digits (0 - 9) and the last two characters are letters (A - Z). How many different identification codes are possible if no characters are allowed to repeat and only vowels can be used? (Note: The vowels are A, E, I, O, and U.)

Question 8

Evaluate the following:

Question 9

There are fifteen sales-people that work for a local company. The company needs to send one sales-person to Hawaii, one sales-person to Florida, and one sales-person to Ohio. No sales-person can go on more than one trip. How many different ways can the company send three of its employees on the
sales trips?

Question 10

A local street vendor asks his customer if she would like to play a game of chance. The vendor has a jar filled with 100 marbles. Of the 100 marbles, 90 are colored black while 10 are colored red. The vendor says that he'll reach in and pick a marble at random. If the marble is black, the street vendor will pay his customer $1, but if the marble is red the customer will pay the street vendor $5. The picked marble is replaced after the game is finished. If this game is played indefinitely, is it more beneficial for the street vendor or the customer? Explain.

Question 11

There are six colors in a bag of M&M's (red, yellow, green, blue, orange, and brown). According to the company's website, the probability of picking a yellow one is 0.14, the probability of picking a green one is 0.14, the probability of picking an orange one is 0.20, and the probability of picking a blue one is 0.24. If the probability of picking a red M&M is equal to the probability of picking a brown one, then what is the probability of picking a brown M&M?

Question 12

There are two $1.00 scratch-off lottery tickets offered at a local convenience store. The first ticket,
Blizzard of Cash, lists the odds of winning as 12 to 15 while the second ticket, Mega Money Meltdown,
lists the odds of winning as 9 to 10. Which of the tickets would be a better deal? Explain.

Question 13

Your dorm building consists of four floors, and you have been tasked with creating a committee which consists of exactly one person representing each floor. The 1st floor has 25 students, the 2nd floor has 28 students, the 3rd floor has 18 students, and the 4th floor has 21 students. How many different
committees could you choose?

Question 14

Your college ID contains an alpha-numeric identification code which the college uses to indentify your meal plan. The code consists of five characters where the first three characters are digits (0 - 9) and the last two characters are letters (A - Z). How many different identification codes are possible if no characters are allowed to repeat?

Question 15

A local street vendor asks his customer if he would like to play a game of chance. The vendor has a jar filled with 100 marbles. Of the 100 marbles, 80 are colored black while 20 are colored red. The vendor says that he'll reach in and pick a marble at random. If the marble is black, the vendor will pay his customer $1, but if the marble is red the customer must pay the street vendor $5. The picked marble is replaced after the game is finished. If this game is played indefinitely, is it more beneficial for the street vendor or the customer? Explain.

Question 16

Your Finite Math teacher gives a three question multiple choice test to her class. Unfortunately you
spent the weekend skiing, so you randomly guess on each question. If there are four choices (A, B, C,
and D) for each question, then what is the probability that you answer all of the questions correctly?
Give your answer as a fraction in reduced form.

Question 17

There are two $1.00 scratch-off lottery tickets offered at a local convenience store. The first ticket,
Blizzard of Cash, lists the odds of winning as 12 to 15 while the second ticket, Mega Money Meltdown,
lists the odds of winning as 8 to 11. Which of the tickets would be a better deal? Explain.

Question 18

After winning student government president, you need to appoint your executive cabinet consisting of the Secretary of Student Affairs, the Secretary of Athletic Affairs, the Secretary of Academic Affairs, and the Secretary of Faculty Affairs. There twelve students from which you must pick four. How many different ways can you appoint the four positions?

Question 19

You spin the spinner shown below four separate times and record the number of times that the spinner lands Blue. Write out the sample space.

Question 20

Your Finite Math teacher gives a three question multiple choice test to her class. Unfortunately you
spent the weekend skiing, so you randomly guess on each question. If there are four choices (A, B, C,
and D) for each question, then what is the probability that you answer exactly one question correctly?
Give your answer as a fraction in reduced form.

Question 21

Simplify:

A) 500
B) 501
C) 1 / 500
D) 1 / 501
E) None of the above.

Question 22

A fair coin is tossed in the air ten times. What is the probability that it will land heads exactly nine times? Give your answer as a fraction in reduced form.

A) 1023/1024
B) 9/10
C) 5/512
D) 3/5
E) None of the above.

Question 23

You toss a coin in the air six times and record the sequence of heads (H) and tails (T). How many outcomes would be in the sample space?

A) 2
B) 8
C) 16
D) 64
E) None of the above.

Question 24

A fair coin is tossed in the air ten times. What is the probability that it will land heads exactly one time? Give your answer as a fraction in reduced form.

A) 5/512
B) 1/2
C) 1023/1024
D) 1/10
E) None of the above.

Question 25

You have 20 vintage concert t-shirts. Sadly your wife is making you throw away all but five of the shirts. How many different groups of shirts can you choose?

A) 56
B) 105
C) 15504
D) 1860480
E) None of the above.

Question 26

You toss two fair six-sided dice and two coins into the air at the same time and record the outcome when they land. What is the probability of the following event? Give your answer as a fraction in
Reduced form.
E1 :"both dice are different and both coins are the same"

A) 1/12
B) 5/12
C) 1/4
D) 11/36
E) None of the above.

Question 27

You are choosing 20 Facebook friends to participate in a Flash-Mod. If you have 850 Facebook friends, then how many different groups of 20 Facebook friends can you choose?

A)
B)
C) 20 !
D) 850 !
E) None of the above.

Question 28

On Valentine's Day you and your date attend a fancy dinner where the following fixed price menu is being served. For $32 per person, your meal includes a choice of appetizer, salad, entrée, and desert. If there are 4 different appetizers, 6 different salads, 8 different entrées, and 3 different deserts to Choose from, then how many different dinner choices are possible? (Note: Assume that you must Choose exactly one from each category.)

A) 21
B) 576
C) 1064
D) 41824
E) None of the above.

Question 29

A scratch-off lottery ticket costs $5.00 to purchase, and it pays out a prize of $0, $5, $10 and $100 with probabilities of 90%, 8%, 1.5% and 0.5%, respectively. What is the expected value of the profit of this Scratch-off lottery ticket?

A) -$4.49
B) -$4.25
C) -$4.08
D) -$3.95
E) None of the above.

Question 30

There are 50 contestants in the Miss America pageant. The judges need to pick 1^st place, 2^nd place, and 3^rd place. How many different ways can the judges choose the arrangement of winners?

A) 19600
B) 125000
C) 15253
D) 117600
E) None of the above.

Question 31

The odds that it will rain tomorrow are 3 to 5. What is the probability that it will rain tomorrow?
(a) 25%
(b) 35%
(c) 60%
(d) 80%
(e) None of the above.

Question 32

A computer password is composed of five characters. If each character must be a letter (A - Z), then how many different passwords can be created which use different vowels for the first three characters And different consonants for the last two characters? (Note: The vowels are A, E, I, O, and U.)

A) 253
B) 7542
C) 25200
D) 589920
E) None of the above.

Question 33

You shoot ten free throws and record the number that you successfully make. How many possible outcomes would be in the sample space?

A) 1024
B) 1023
C) 10
D) 11
E) None of the above.

Question 34

You toss two fair six-sided dice and two coins into the air at the same time and record the outcome when they land. What is the probability of the following event? Give your answer as a fraction in
Reduced form.
E1 :"both dice are the same and both coins are the same"

A) 1/9
B) 13/36
C) 5/18
D) 1/12
E) None of the above.

Question 35

The chance that it will rain tomorrow is 30%. Thus, the odds that it will rain tomorrow are what?

A) 30 to 100
B) 3 to 7
C) 30 to 1
D) 5 to 6
E) None of the above.

Question 36

On Valentine's Day you and your date attend a fancy dinner where the following fixed price menu is being served. For $32 per person the meal includes your choice of appetizer, salad, entrée, and desert. If there are 5 different appetizers, 3 different salads, 7 different entrées, and 4 different deserts to Choose from, then how many different dinner choices are possible? (Note: Assume that you must Choose exactly one from each category.)

A) 350
B) 420
C) 684
D) 1425
E) None of the above.

Question 37

You have 800,000 people who follow you on Twitter. You would like to choose a president, a vicepresident and a secretary from your 800,000 followers to form a Fan-Club. How many different ways could this be done, realizing that order of the choices will matter?

A)
B)
C) 800000 !
D) 3 !
E) None of the above.

Question 38

Simplify:

A) 501/500
B) 500 / 499
C) 500 / 501
D) 499 / 500
E) None of the above.

Question 39

A scratch-off lottery ticket costs $1.00 to purchase, and it pays out a prize of $0, $1, $5 and $10 with probabilities of 85%, 12%, 2% and 1%, respectively. What is the expected value of the profit of this Scratch-off lottery ticket?

A) -$0.88
B) -$0.73
C) -$0.68
D) -$0.56
E) None of the above.

Question 40

A computer password is composed of seven characters. If each character must be a letter (A - Z), then how many different passwords can be constructed so that the password is the same both forwards and Backwards? (Note: Examples would be ETTFTTE or RACECAR.)

A) 245712
B) 358800
C) 456976
D) 5866254125
E) None of the above.