Lesson 2.2.1
2-69. Find the probability of each event. Write your answer as a fraction and as a percent.
a. Drawing a diamond from a standard deck of cards.
b. Rolling a number less than five on a standard number cube.
c. Drawing a blue marble from a bag of 18 marbles, three of which are blue.
[ a: 13/52 or 25%, b: 4/6 or 66.67%, c: 3/18 or 16.67% ]
2-70. Imagine a standard deck of cards with all of the
aces and twos removed. Find each probability below.
a. P(heart) b. P(black) c. P(face card)
d. How is the P(face card) different with this deck from the probability if the deck was not missing any cards? Which probability is greater? Why?
e. P(not heart)
[ a: 11/44 , b: 22/44 , c: 12/44 , d: P(face card) with a normal deck is 12/52 . It is more likely to draw a heart in the modified deck because there are fewer non-face cards. e: 33/44 ]
2-71. Larry and Barry are playing a game using a penny and a number cube. Larry gets a point for every “three” that is rolled. Barry gets a point for every “head” that is flipped. Is this game fair? Why or why not? [ No, it is not fair, because Larryhas only a 1 in 6 chance of getting a point, while Barry has a 1 in 2 chance ofgetting a point. ]
2-72. Steve and Cathy are playing a card game with a standard deck of 52 playing cards.Cathy is dealt an ace and a four. Steve is dealt a jack.
a. How many cards are left in the deck? [ 49 ]
b. How many of the remaining cards are aces? [ 3 ]
c. If Steve gets an ace, he will win. What is the probability that he will get an ace on the next card he is dealt? [ 3/49 ]
d. Next Steve gets a two and Cathy gets a five. What is the probability that Steve
will get a nine on the next card he is dealt? [ 4/47 ]
2-73. There are 18 chocolate chip cookies, 12 oatmeal cookies, and 10 raisin cookies in a cookie jar. Miguel takes a cookie from the jar without looking.
a. What is the complement of getting a chocolate chip cookie?
[ Not getting a chocolate chip cookie. Or: Getting a oatmeal or raisin cookie. ]
b. What is the probability of part (a)? Show your work to support your answer.
[ 22/40 = 55% ]
2-74. Marissa is drawing erasers from a bag containing 6 pink erasers, 2 yellow erasers,5 green erasers, and 3 purple erasers.
a. What is the probability that she will draw a pink eraser?
b. If one yellow, two green, and one purple eraser are added to the bag, what is thenew probability that she will draw a pink eraser?
c. In which situation is it more likely that she will draw a pink eraser?
[ a: 6/16 , b: 6/20 , c: Before the other erasersare added, since 6/16 30/806/20 24/80 . ]
Lesson 2.2.2
2-79. A BETTER CHANCE OF WINNING
Each of the problems below describes two different games you can play with a
random number generator. In each case, you will win if the random number
generator gives you the indicated kind of number. Find the theoretical probability
that you win each game below. Decide and justify whether Game I or Game II in
each part gives you a better chance of winning.
[ a: 8/20 4/20 , Game I; b: 4/20 8/40 , equal chance; c: 5/40 4/25 or12.5% 16%, Game II. ]
Game I Game II
a. Picking a prime number from the
integers between 1 and 20
b. Picking a multiple of 5 from the
integers between 1 and 20
c. Picking a multiple of 7 from the
integers between 1 and 40
Picking a prime number from the
integers between 21 and 40
c. Picking a multiple of 5 from the
integers between 1 and 40
Picking a multiple of 6 from the
integers between 1 and 25
2-80. If you used a random number generator for the numbers from 1 through 20 to play a
game, what is the theoretical probability of getting each of these outcomes?
a. A multiple of three or a multiple of 7, P(multiple of 3 or multiple of 7)
b. P(even or odd)
c. P(prime or 1)
d. How did you find the probabilities of these events? Be ready to share your ideas with the class.
[ a: 8/20 , b: 1, c: 9/20 , d: Answers will vary. ]
2-81. Nicole has a random number generator that will produce the numbers from 1 through 50 when she pushes a button. If she pushes the button, what is:
a. P(multiple of 10) ?
b. P(not 100) ?
c. P(not a multiple of 4)?
d. P(one-digit number) ?
[ a: 5/50 , b: 1, c: 38/50 , d: 9/50 ]
Lesson 2.2.3
2-88. For each of the following probabilities, write “dependent” if the outcome of the
second event depends on the outcome of the first event and “independent” if it does not.
a. P(spinning a three on a spinner after having just spun a two) [ independent ]
b. P(drawing a red six from a deck of cards after the three of spades was just drawn and not returned to the deck) [ dependent ]
c. P(drawing a face card from a deck of cards after a jack was just drawn and replaced and the deck shuffled again) [ independent ]
d. P(selecting a lemon-lime soda if the person before you reaches into a cooler full of lemon-lime sodas, removes one, and drinks it) [ independent ]
2-89. Skye’s Ice Cream Shoppe is Mario’s favorite place to get ice cream. Unfortunately,because he was late arriving there, his friends had already ordered. He did not knowwhat they ordered for him. They told him that it was either a waffle cone or a sundaeand that the ice cream flavor was apricot, chocolate, or blackberry.
a. Make a list of all the possible ice cream orders. [ WA, WC, WB, SA, SB, SC ]
a. What is the probability that Mario will get something with apricot ice cream? [ 1/3 ]
b. What is the probability that he will get a sundae? [ 1/2 ]
c. What is the probability that he will get either something with chocolate or a
waffle cone with blackberry? [ 1/3 1/6 1/2 ]
d. What is the probability that he will get orange sherbet? [ 0 ]
Lesson 2.2.4
2-96. Maggie was at the State Fair and decided to buy a sundae from an ice-cream stand. The ice-cream stand had four flavors of ice cream (chocolate, vanilla, mint chip, and coconut) and two toppings (hot fudge and caramel). How many different sundaes could Maggie create using one scoop of ice cream and one topping? Make a table to support your answer.
[ 8 possible sundaes. ]
2-97. The spinner at right is spun twice. Make a table, and calculate
the probability of each of the following outcomes.
a. Getting black twice.
[ 1/3 1/3 1/9 ]
b. Getting green twice.
[ 1/3 1/3 1/9 ]
2-98. Imagine spinning the spinner at right.
- What is the probability you will spin a P or a Q on your first spin?
[ 2/4 1/2 ]
b. Find all of the possible outcomes of spinning the spinner twice by making a table or a list. What is the probability you will spin a P on your first spin and then a Q on your second spin? Explain how you decided.
[ 1/16 ; Sample reasoning:There are 4 x 4 = 16 possible outcomes. ]
Lesson 2.2.5
2-104. WALKING THE DOG
Marcus and his brother always argue about who will walk the dog. Their father wants to find a random way of deciding who will do the job. He invented a game to help them decide. Each boy will have a bag with three colored blocks in it: one yellow, one green, and one white. Each night before dinner, each boy draws a block out of his bag. If the colors match, Marcus walks the dog. If the two colors do not match, his brother walks the dog. Marcus’ father wants to be sure that the game is fair. Help him decide.
a. Make a probability tree of all of the possible combinations of draws that Marcus
and his brother could make. How many possibilities are there?
[ 9 possibilities: YY, YG, YW, GY, GG, GW, WY, WG, and WW. ]
b. What is the probability that the boys will draw matching blocks? Is the game
fair? Justify your answer.
[ P(match)= 3/9 . The game is not fair. ]
2-105. For Shelley’s birthday on Saturday, she received:
Two new shirts (one plaid and one striped);
Three pairs of shorts (tan, yellow, and green); and,
Two pairs of shoes (sandals and tennis shoes).
On Monday she wants to wear a completely new outfit. How many possible outfit choices does she have from these new clothes? Draw a diagram to explain your reasoning.
[ 12 possible outfits ]
2-106. Alan is making a bouquet to take home to his grandmother. He needs to choose onekind of greenery and one kind of flower for his bouquet. He has a choice of ferns or leaves for his greenery. His flower choices are daisies, carnations, and sunflowers.
a. Draw a tree diagram to show the different bouquets he couldmake. How many are there?
[There are 6 possible bouquets. ]
- What is the probability he will use ferns?
[ 1/2 ]
- What is the probability he will not use sunflowers?
[ 2/3 ]
Lesson 2.2.6
2-115. Lucas is having yogurt and an apple for a snack. There are five containers of yogurt in the refrigerator: three are raspberry, one is vanilla, and one is peach. There are also two green apples and three red apples.
a. If he reaches into the refrigerator to get a yogurt without looking, what is the probability Lucas will choose a raspberry yogurt?
b. What is the probability he will choose a red apple if it is the first item he selects?
c. What is the probability Lucas will eat a raspberry yogurt and a red apple?
[ a: 3/5 , b: 3/5 , c: 9/25 ]
2-116. A bag contains 3 red, 5 yellow, and 7 purple marbles. Find the probability of drawing a purple marble followed by a red marble. The first marble is put back in the bag between draws.
[ 21/225 ]
2-117. At the school fair, students play a game called Flip and Spin, in which a player first flips a coin and then spins the spinner shown at right. If the coin comes up heads and the spinner lands on red, the player wins a stuffed animal. If the coin comes up tails and the spinner lands on yellow, the player gets another turn to play. If the spinner lands on green, the player’s turn is over (whether the coin comes up heads or tails).
a. Calculate the probability that you will win a stuffed animal on the first play. Also find the probability of getting another turn and of losing your turn. Use more than one method to show your thinking. Be prepared to share your strategies with the class.
[ The probability forwinning a stuffed animal is 1/6 . Theprobability of getting another turn isalso 1/6 and the probability for losingis 4/6 2/3 . ]
b. How would the outcomes change if someone were to spin first and then flip the
coin? How would the outcomes change if someone was to spin and anotherperson was to flip a coin at the same time? Explain.
[ The outcomes would notchange. The coin flip and spin are independent events. ]
2-118. Find the probability of each of the outcomes of compound events described below.
a. Flipping a coin and getting “heads” and picking a Jack from a standard deck ofcards.
[ 1/2 1/13 1/26 ]
b. Rolling a five on a number cube and then rolling a six.
[ 1/6 1/6 1/36 ]
c. Flipping a coin and getting “tails” and then choosing the one blue marble in abag of 12 marbles.
[ 1/2 1/12 ]
d. Picking the Ace of Spades from a standard deck of cards, putting it back, mixingthem up and picking the Ace of spades again.
[ 1/52 1/52 1/2704 ]