Section 12.3 – Probability
P(success) =
Name __________________________________________
P(failure) =
1. A box contains 2 baseballs, 7 softballs, and 11 tennis balls. What is the probability that a ball selected at random will be a
tennis ball? A baseball? A softball? Not a softball? Not a tennis ball?
2. Two dice are thrown. List all of the possible sums of the two dice by completing the chart.
3. Use the chart from #2 to find the probability that one roll of the two dice will give…..
(a) a sum of 7
(b) two 6’s
(c) a sum of 8
(d) a sum less than 5
+
1
2
3
4
5
6
1
2
3
4
5
4. You have 10 songs in a play list, which you set to play the songs at random. All 10 songs will be played without repeats.
(a) What is the probability that the songs are played in the same order that they are listed on your playlist?
(b) You have 4 favorite songs on the playlist. What is the probability that 2 of your favorite songs are played as the first
two songs, in any order?
Odds
Odds of a Successful Outcome =
Odds of an Unsuccessful Outcome =
5. Glenn Schwartz announced that the probability of snow tomorrow is 3/10. Find the odds that it will snow tomorrow. Find
the odds that it will not snow tomorrow.
6. The probability that Patriots will win next year’s Super Bowl is 4/5. Find the odds that the Patriots will win the Super Bowl.
Find the odds that the Patriots will not win the Super Bowl.
7. The odds of a horse winning the Kentucky Derby are 1:12. What is the probability the horse will win the race? What is the
probability the horse will not win the race?
Classwork – Probability/Odds
1. State the odds of an event occurring given the probability.
(a) 1/2
(b) 3/4
(c) 7/15
(d) 3/20
2. State the probability of an event occurring given the odds of the event.
(a) 3/4
(b) 6/5
(c) 4/9
(d) 1/1
3. The odds are 7 to 5 that the Broncos will win the Super Bowl. What is the probability that they will win?
4. The probability of Jason getting accepted at the University of Pennsylvania is 3/4. What are the odds that we will NOT get
accepted?
5. When Steve plays John in a video game, the odds that Steve wins are 4/3. What he the probability that Steve will win the
next three games?
6
Section 12.4 – Probability of Compound Events
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Name __________________________________________
When you consider all the outcomes for either of two events A and B, you form the union of A and B.
When you consider only the outcomes shared by both A and B, you form the intersection of A and B.
The union or intersection of two events is called a compound event.
Mutually Exclusive vs. Inclusive Events (“OR”)
Mutually Exclusive – where there is no intersection of events A and B (they have no outcomes in common)
P(A or B) = P(A) + P(B)
Mutually Inclusive – when there is an intersection of events A and B (they share at least one outcome)
P(A or B) = P(A) + P(B) – P(A and B)
1. Dana has 4 pennies, 3 nickels, and 6 dimes in her pocket. She takes one coin from her pocket at random. What is the
probability that it is a penny or a dime?
2. Two faces of a die are red, two are blue, and two are white. The die is tossed. Find the probability that the die shows either
red or blue. Find the probability that the die does not show red.
3. In a homeroom, 5 of the 12 girls have blonde hair and 2 of the 16 boys have blonde hair. What is the probability of randomly
selecting a boy or a blonde-haired person as homeroom representative to the student council?
4. A card is randomly selected from a deck. What is the probability that it is an ace or a face card?
5. A card is randomly selected from a deck. What is the probability that is a red card or a face card?
6. Last year, a company paid overtime wages or hired temporary help during 9 months. Overtime wages were paid during 7
months and temporary help was hired during 4 months. At the end of the year, an auditor examines the accounting records
and randomly selects one month to check the company’s payroll. What is the probability that the auditor will select a month
in which the company paid overtime wages and hired temporary help?
Complement – the event A (read as “A prime”), called the complement of event A, consists of all outcomes that are NOT in
event A. The probability of the complement of A is P( A)  1  P( A)
7. When two six-sided dice are tossed, there are 36 possible outcomes. Find the probability that…
(a) the sum is not 8.
(b) the sum is greater than or equal to 4.
Section 12.5 – Probability of Independent and Dependent Events
Name _______________________________________
Independent vs. Dependent Events (“AND”)
Independent Events – the occurrence of one event has no effect on the occurrence of the other
P( A and B)  P( A)  P( B)
Dependent Events – the occurrence of one event affects the occurrence of the other
P( A and B)  P( A)  P( B | A)
1. A green die and a red die are tossed. What is the probability that a 4 shows on the green die and a 5 shows on the red die?
2. Find the probability of getting a sum of 7 on the first toss of two dice and a sum of 4 on the second toss of the dice.
3. Tom has 4 navy socks and 6 black socks in a drawer. His power is out, and he randomly pulls two socks out of the drawer.
What is the probability that he will select a pair of navy socks? (ie: Navy and Navy)
4. There are 2 glasses of root beer and 4 classes of cola on the counter. Dave drinks two of them at random. What is the
probability that he drank 2 glasses of cola? (ie: Cola and Cola)
5. Two cards are drawn at random from a deck of 52 cards. What is the probability that both are hearts? Both are 4’s?
(ie: heart and heart; 4 and 4)
6. A bag contains 4 red, 4 green, and 7 blue marbles. Three are selected without replacement. What is the probability of
selecting a red marble, then a green marble, then a blue marble? (ie: red and green and blue)
Classwork – Mutually Exclusive/Inclusive and Independent/Dependent
1. Of 17 students in a class, 5 have blue eyes. Two students are chosen at random. Find the probability and odds of having…
(a) both students have blue eyes
(b) neither student has blue eyes
2. There are 5 pennies, 7 nickels, and 9 dimes in a jar. Suppose that 2 coins are to be selected at random. Find the chance of…
(a) selecting 2 pennies if no replacement occurs
(b) selecting 2 pennies if replacement occurs
3. Michael’s family is preparing to move to a new home. Michael is helping his mother pack. There are 5 clocks, 5 candles,
and 6 picture frames randomly place on a table waiting to be boxed. Michael accidentally knows two items off the table and
breaks them. What is the probability that he broke…
(a) 2 picture frames
(b) 2 clocks
(c) a clock, then a candle
(d) a clock and a candle
4. If two dice are tossed, what is the probability of getting…
(a) a sum of 6 or a sum of 9
(b) either die will show a 2
5. John has 5 rap, 9 rock, and 4 country songs on a playlist on his i-pod. If he randomly selects 2 different songs, what is the
probability that he gets…
(a) 2 rap
(b) 2 rock
(c) 2 country
(d) a rap, then a rock
(e) 1 rap and 1 rock
6. A card is drawn from a standard deck. What is the probability of drawing…
(a) a king or a queen
(b) an ace or a red card
7. Suppose you select 2 letters at random from the word ALGEBRA. Find the probability of getting…
(a) 2 consonants
(b) 2 vowels
(c) a consonant, then a vowel