Warm Up

1
Warm Up
Tyler has a bucket of 30 blocks. There are 8
cubes, 6 cylinders, 12 prisms and 4 pyramids.
1) What is the theoretical probability () of
drawing a cube out of the bucket? 2) If Tyler
continues drawing blocks and putting them back
in 40 times, and pulls a cube 12 times, what is
the experimental probability ()of pulling a
cube? 3) Why are the probabilities ()
different?
2

• An experiment consists of rolling two fair number
  cubes. Find each probability.
• P(rolling two 3s)
• 2. P(total shown gt 10)

3
Learn to find the probabilities of independent
and dependent events.
4
Insert Lesson Title Here
Vocabulary
compound events independent events dependent
events
5
A compound event is made up of one or more
separate events. To find the probability of a
compound event, you need to know if the events
are independent or dependent.
Events are independent events if the occurrence
of one event does not affect the probability of
the other. Events are dependent events if the
occurrence of one does affect the probability of
the other.
6
Determine if the events are dependent or
independent. (Hint Does the first even have
any effect on the second event?) A. getting
tails on a coin toss and rolling a 6 on a number
cube B. getting 2 red gumballs out of a gumball
machine
7
Determine if the events are dependent or
independent. (Hint Does the first even have any
effect on the second event?) A. rolling a 6 two
times in a row with the same number cube B. a
computer randomly generating two of the same
numbers in a row
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
What is the probability that when you roll the
dice, and spin the spinner that you get a 3 on
each?
12
If you roll the dice, what is the probability
that you will get an even number on both dice?
13
Three separate boxes each have one blue marble
and one green marble. One marble is chosen from
each box. What is the probability of choosing a
blue marble from each box?
14
Three separate boxes each have one blue marble
and one green marble. One marble is chosen from
each box. What is the probability of choosing a
blue marble, then a green marble, and then a blue
marble?
15
One box contains 4 marbles red, blue, green, and
black. What is the probability of choosing a
blue marble, replacing it, and pulling blue again?
16
Jared is going to perform an experiment in which
he spins each spinner once. What is the
probability that the first spinner will land on
A, the second spinner will land on an even
number, and the third spinner will land on Blue?
Express your answer as a fraction in simplest
form.
17
Jean spins two spinners. Find the probability
that the first spinner will NOT show an even
number and that the second spinner will NOT show
an odd number. Express your answer as a fraction
in simplest form.

18
One box contains 4 marbles red, blue, green, and
black. What is the probability of choosing a
blue marble, not replacing it and then pulling a
red? How is this problem different from the
others? How do you think this will change the
way we work the problem?
19
To calculate the probability of two dependent
events occurring, do the following 1. Calculate
the probability of the first event. 2. Calculate
the probability that the second event would
occur if the first event had already occurred.
3. Multiply the probabilities.
20
The letters in the word dependent are placed in a
box. If two letters are chosen at random, what is
the probability that they will both be
consonants? (Without replacement)
21
The letters in the word dependent are placed in a
box. If two letters are chosen at random, what
is the probability that they will both be both be
vowels? (Without replacement)
22
(No Transcript)
23
The letters in the phrase I Love Math are placed
in a box. If two letters are chosen at random,
what is the probability that they will both be
consonants? (Without replacement)
24
The letters in the phrase I Love Math are placed
in a box. If two letters are chosen at random,
what is the probability that they will both be
vowels? (Without replacement)
25
Insert Lesson Title Here
Lesson Quiz
Determine if each event is dependent or
independent. 1. drawing a red ball from a bucket
and then drawing a green ball without replacing
the first 2. spinning a 7 on a spinner three
times in a row 3. A bucket contains 5 yellow and
7 red balls. If 2 balls are selected randomly
without replacement, what is the probability
that they will both be yellow?
dependent
independent
26
WARM UP
The Venn diagram below shows how many of the 500
students at Hayes Middle school watched only the
Olympics, watched only the All-Star Basketball
game, or watched both events.
What is the probability that a student randomly
selected while walking in the hall watched the
Olympics that weekend? Justify your solution.
27
What is the probability that a student randomly
selected while walking in the hall watched the
All-Star Basketball game that weekend? Justify
your solution. What is the probability that a
student randomly selected while walking in the
hall watched neither the Olympics nor the
All-Star Basketball game that weekend? Justify
your solution.
28
A fair number cube and a coin are used to collect
data. The faces of the cube are colored red,
green, blue, orange, yellow, and purple. What
is the probability of rolling a green or a
yellow, and then flipping the coin and getting
heads?
29
Joe has 11 markers in a backpack. One of them is
dark brown and one is tan. Find the probability
that Joe will reach into the backpack without
looking and grab the dark brown marker and then
reach in a second time and grab the tan marker.
Express your answer as a fraction in simplest
form.
30
Jake the magician has the following items in his
hat 1 scarf, 2 rabbits, 2 doves, and 2 bouquets
of flowers. The magician draws 1 item and does
not replace it before drawing a second item. What
is the probability of the magician drawing a
rabbit and then a dove out of his hat?
31
Sarah is playing a game with 3 six-sided number
cubes. Each cube is numbered 1 through 6. If
Sarah rolls 3 ones, she will lose all of
her points. What is the probability that she will
roll 3 ones?
32
Jordan wants the probability of drawing a blue
tile and then drawing a second blue tile to be
1/28, if the first blue tile is not replaced. If
there will only be 2 blue tiles in the bag, how
many total tiles should be placed in the bag?
33
The 6 cards below were placed in a bag.
A card is randomly drawn from the bag and not
replaced. What is the probability of drawing an
O card and then drawing another O card?
34
Derek placed 2 red tiles, 10 blue tiles, 5 green
tiles, and 3 yellow tiles in a bag. He challenged
his friends to draw randomly the 2 red tiles from
the bag. Susan accepted the challenge. She drew
one tile, did not replace it, and drew a second
tile. What is the probability that Susan will
draw 2 red tiles?
35
You have a bag that contains 7 candies 3 mints,
2 butterscotch drops, and 2 caramels, with the
candies thoroughly mixed. Which of the
following statements are true? Which are not
true? Justify your solutions.