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 Larry has only a 1 in 6 chance of getting a point, while Barry has a 1 in
2 chance of getting 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 the new
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 erasers are added, since 6/16 30/80 6/20 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 or 12.5% 16%, Game II. ]
Game I
Game II
a. Picking a prime number from the
Picking a prime number from the
integers between 1 and 20
integers between 21 and 40
b. Picking a multiple of 5 from the
c. Picking a multiple of 5 from the
integers between 1 and 20
integers between 1 and 40
c. Picking a multiple of 7 from the
Picking a multiple of 6 from the
integers between 1 and 40
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 know what they ordered for him. They told
him that it was either a waffle cone or a sundae and 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.
a. 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 one kind 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 could make. How many are there?
[ There are 6 possible bouquets. ]
b. What is the probability he will use ferns?
[ 1/2 ]
c. 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 for winning a stuffed animal is 1/6 . The probability of getting
another turn is also 1/6 and the probability for losing is 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 another person was to flip a
coin at the same time? Explain.
[ The outcomes would not change. 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 of cards.
[ 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 a bag of 12
marbles.
[ 1/2 1/12 ]
d. Picking the Ace of Spades from a standard deck of cards, putting it back, mixing them up and
picking the Ace of spades again.
[ 1/52 1/52 1/2704 ]
http://www.cpm.org/pdfs/standards/stats/Stats%20Unit%202%20TV.pdf