Download 10.2-Probability of Events

Chapter 10
10.2: Finding Probability of Events
Objective…
Key Vocabulary…
Probability
Fair
Biased
Mutually Exclusive
Complementary Events
Complement
Part A: Use Probability to Describe the Likelihood of an Event
Probability can be expressed as a
Words that describe
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0%
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50%
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100%
Probability Number Line
Chapter 10
10.2: Finding Probability of Events
1) Find the probability of an event when flipping a fair coin.
a. What is the probability that it will land on heads?
b. What is the probability that the coin will land on both heads
and tails?
2) You roll a fair number cube.
a. Find the probability of getting a 4.
b. Find the probability of getting a 7.
3) When you spin the spinner, what is the probability that the arrow will
point to a number?
Part B: Find the Probability of an Event
Probability Notation
Example…
Chapter 10
10.2: Finding Probability of Events
•
1)
Find the probability of an event
A pebble is picked at random from a bag containing 6 gray pebbles,
9 white pebbles, and 5 tan pebbles. Let B be the event of picking a
white pebble.
a. Find the probability that event B will occur.
b. Express your answer as a fraction, decimal, and percent.
2)
Max has 4 short-sleeved shirts and 5 long-sleeved shirts in his
closet. X is the event of Max randomly choosing a long-sleeved
shirt. Find P(X). Express your answer as a fraction, decimal, and
percent.
3)
A box contains 28 pink ribbons and 12 green ribbons. You randomly
take a ribbon from the box without looking. Find the probability of
picking a pink ribbon. Express your answer as a fraction, decimal,
and percent.
Part C: Use Venn Diagrams to Show Relationships for Events
Mutually Exclusive
NOT Mutually Exclusive
E is the event of rolling an even number
Flipping a coin
F is the event of rolling a number grater
than 3
Why?
Why?
Chapter 10
10.2: Finding Probability of Events
•
1)
Represent mutually exclusive events with a Venn Diagram
Ten cards, each printed with a different whole number form 16 to 25,
are shuffled and placed face down. A card is drawn at random from the
ten cards. Let A be the event of getting a number that is a multiple of 3.
Let B be an event of getting a number that is a multiple of 5.
a. List all the outcomes favorable to events A and B.
b. Draw a Venn Diagram for the sample space. Place all possible
outcomes in the Venn Diagram.
c. Are events A and B mutually exclusive? Explain.
d. Find P(A) and P(B).
2)
Ten cards have the following numbers printed on them: 3, 6, 9, 11, 19, 27,
35, 39, 40, and 45. A card is randomly drawn from the ten cards. Let W
be the event of getting a number that is an odd number greater than 20.
Let V be the event of getting a prime number.
a. List all the outcomes favorable to events W and V.
b. Draw a Venn Diagram for the sample space and the two events.
Place all possible outcomes in the Venn Diagram.
c. Are events W and V mutually exclusive? Explain.
d. Find P(W) and P(V).
Chapter 10
10.2: Finding Probability of Events
•
1)
Represent non-mutually exclusive events using a Venn Diagram
A name is randomly chosen from a list of names: Bill, Jesse, Eva, Chloe,
Mary, Ruth, Kim, Henry, Elsa, and Sean. Let X be the vent of choosing a
name with two vowels. Let Y be the event of choosing a name made of
three letters.
a. Draw a Venn Diagram for the sample space and the two events.
b. Place all possible outcomes in the Venn Diagram.
c. Are events X and Y mutually exclusive? Explain.
d. Find P(X) and P(Y).
2)
A letter is selected at random from the state name “Rhode Island”. Let
C be the event of getting a consonant. Let H be the event of getting a
letter that comes after “H” in the alphabet.
a. Draw a Venn Diagram for the sample space and the two events.
Place all possible outcomes in the Venn Diagram.
b. Are events C and H mutually exclusive? Explain.
c. Find P(C) and P(H).
Chapter 10
10.2: Finding Probability of Events
Part D: Define Complementary Events
Meaning of Complement
Notation
Picture
Math Reasoning
• Find the probability of a complementary event
1)
A basket contains 18 red flowers and 12 white flower petals. A
flower petal is randomly picked from the basket. Let W be the
event of picking a white flower petal.
a. Draw a Venn diagram to represent events W and W’. Give the
meaning of the event W’, the complement of event W.
b. Find P(W) and P(W’)
2)
You randomly choose a month from the twelve months in a year.
Let A be the event of randomly choosing a month that has the
letter “a” in its name.
a. Draw a Venn diagram to represent events A and A’. Give the
meaning of the event A’, the complement of event A.
b. What outcomes are favorable to event A’?
c. Find P(A) and P(A’)
Chapter 10
10.2: Finding Probability of Events
•
1)
Solve a probability problem involving percents
25% of the students in the school band play brass instruments. Among
the brass players, 20% play the trombone. The band director randomly
chooses a band member to play a solo.
a. Draw a Venn diagram to represent the information:
b. What is the probability that a band member who does not play a
brass instrument is selected?
c. What is the probability that a trombone player is selected?
2)
40% of the apples in an orchard are green and the rest of the apples are
red. 5% of the red apples are rotten.
a. Draw a Venn diagram to represent the information:
b. If you pick an apple at random in the orchard, what is the probability
the apple you pick is red that is not rotten? Answer as a fraction,
decimal, and percent.
Chapter 10
10.2: Finding Probability of Events
• Solve a probability problem involving a ratio
1)
Out of 500 students, 156 students study Spanish as a foreign
language. Of those studying Spanish, 1 out of 6 students also
study French.
a. Draw a Venn diagram to represent the information.
b. What fraction of the students studied both Spanish and
French?
c. If a student is selected at random from 500 students, what is
the probability that student who studies both Spanish and
French is selected? Answer as a fraction, decimal, and percent.
2)
Among the 200 jellybeans in a bag, 3 out of every 5 are blue
jellybeans. The blue jellybeans consist of light blue ones and dark
blues ones in the ratio 2 : 1.
a. Draw a Venn diagram to represent the information.
b. What fraction of the jellybeans are light blue?
c. If you pick a jellybean randomly from the bag, what is the
probability that a jellybean that is light blue is selected?
Answer as a fraction, decimal, and percent.