Download Geometry Unit 4 - Clark Magnet High School

Geometry Unit 4
Probability and Statistics 2
2 May 2016
Agenda 5/2/2016
● Probability Review - Sample Space, Events and Notation Tell me about independent and dependent events and
then self- corrections
● Vocabulary and Notation Practice p. 14
● The Addition Rule - Task
● Homework:
Probability Review Questions continued
3) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die
is rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
List the sample space below - this is for the compound event where we first toss a
coin and then roll the die.
S=
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
Note that there are 12 outcomes in the sample space (2 x 6 = 12)
1pt
Probability Review Questions continued
4) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die
is rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Are these independent or dependent events?
Explain.
2pts
Probability Review Questions continued
4) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die
is rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Are these independent or dependent events? Explain.
The outcome of rolling the die has nothing to do with the outcome
of tossing the coin, neither event depends on the outcome of the
other one, so these are independent events.
2pts
Probability Review Questions continued
5) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die
is rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Find each probability.
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H,
6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
a) P(heads and six) = 1/12 = 0.083 = 8.3%
Also notice that ½ x ⅙ = 1/12
Probability Review Questions continued
5) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die
is rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Find each probability.
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
b) P(tails and even) = 3/12 = ¼ = 0.25 = 25%
½ x 3/6 = 3/12
Probability Review Questions continued
5) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die i
rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Find each probability.
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
c)P(heads and a number less than 3) = 2/12 = ⅙ = 0.16 = 16.6%
½ x 2/6
Probability Review Questions continued
5) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die i
rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Find each probability.
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
d)P(tails and 3) = 1/12 = 0.083 = 8.3%
Probability Review Questions continued
5) A coin is tossed (can be heads or tails, 2 possible outcomes), then a six sided die i
rolled (1, 2, 3, 4, 5, 6,) are the six possible outcomes.
Find each probability.
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
e)P(heads and a number greater than 2) = 4/12 = ⅓ = 0.33 = 33.3%
5pts for qu 5
6. One bag contains 3 red and 4 white balls. (7)
A second bag contains 6 yellow, and 3 green balls
(9). One ball is drawn from each bag.
a) P(red and yellow) = 3 x 6
7
9
= 18 = 2 = 0.286
63
7
6. One bag contains 3 red and 4 white balls. (7)
A second bag contains 6 yellow, and 3 green balls
(9). One ball is drawn from each bag.
b) P(white and not green) = 4 x 6
7
= 0.38 or 38%
9
= 24 = 8 =
63
21
6. One bag contains 3 red and 4 white balls. (7)
A second bag contains 6 yellow, and 3 green balls
(9). One ball is drawn from each bag.
c) P(red and green) = 3 x 3
7
9
=9 = 1 =
63
7
= 0.143 or 14.3%
3pts for qu 6
7.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue.
Keith selects two cards from the deck and does
not replace them. Are the event of drawing the
first card and the event of drawing the second
card independent or dependent events? Explain.
7.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue.
Selecting two cards from the deck are dependent
events. When Keith removes the first card he
leaves behind fewer cards to choose from on the
next draw. The probability of the second event
depends on what happened during the first event.
2pts for qu 7
8.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue. Select 2 cards,
without replacing.
a)
P(a 5 and then a 9) = 4 x 4 = 4
40 39 390
0.0102 =1.02%
8.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue. Select 2 cards,
without replacing.
b) P(two 7s) = 4 x 3 = 3
= 1/130 0.0077 =0.77%
40 39 390
8.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue. Select 2 cards,
without replacing.
c) P(orange then a blue) = 10 x 10 = 10
40
39
=5
156
0.064 , or 6.4%
78
8.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue. Select 2 cards,
without replacing.
d) P(orange10 then a blue 8) = 1 x 1 = 1
40
39 1560
0.00064 , or 0.064%
8.Keith makes up a deck of 40 cards. The cards are
numbered from 1 to 10 and each number has a
color: orange, red, black and blue. Select 2 cards,
without replacing.
e) P(7 then a red 5) = 4 x 1 = 1
40
39
=
390
0.00256 , or 0.256%
5 pts for qu 8
9. If you toss a coin six times, what is the probability
of it landing on heads every time?
½ x ½ x ½ x ½ x ½ x ½ = 1 / 26 = 1 / 64
2 pt for qu 9 if
show work
Your name
5/2/2016
Probability Review Questions Continued
Turn in to Roupen for score to be recorded.
/ 20
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes.
1) If one item is chosen at random,
P(marble) =
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
1) If one item is chosen at random,
P(marble) = 30 /40 = ¾ = 0.75 or 75%
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
2) If one item is chosen at random,
P(quarter) =
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
2) If one item is chosen at random,
P(quarter) = 4 /40 = 1/10 = 0.1 or 10%
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
3) If one item is chosen at random,
P(Red U White) = look up what U stands for here
on pg. 13
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
3) If one item is chosen at random,
P(Red U White) =15 red + 5 white + 4 white + 6red
40 items in the bag
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
3) If one item is chosen at random,
P(Red U White) =30 = ¾ = 0.75 = 75%
40
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
4) If one item is chosen at random,
P(Red Coin) =
What does mean?
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
4) If one item is chosen at random,
P(Red Coin) = 6/40 = 3/20
or 15%
Red item that is also a coin, has to be both
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
5) If one marble is drawn,
P(Red U blue) = 15 + 10 = 25/30 = ⅚ or 83%
30
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
6) If one coin is drawn,
P(dime) = 6 = ⅗
10
or 60%
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
7) If one item is chosen at random,
P(coin|white) =
Meaning?
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
7) If one item is chosen at random,
P(coin|white) = Meaning? “Coin given it is white”
coin only looking at white items
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
7) If one item is chosen at random,
P(coin|white) =
4 white quarters
Coin given it is white 5+ 4 white items
= 4/9 or 44%
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
8) If one item is chosen at random,
P(white|coin) =
white given it is a coin
Vocabulary and Notation Practice Problems pg 14
A bag contains 30 marbles: 15 red, 10 blue and 5
white.
It also contains 10 coins: 4 white quarters, and 6
red dimes. 40 items altogether.
8) If one item is chosen at random,
P(white|coin) =
white given it is a coin
4 = ⅖ or 40%
10
Vocabulary and Notation Practice Problems pg 14
Steven was looking at some data and noticed that
50% of the school was male and that 20% of
students participated in a sport. He concluded that
P(Male U Sport) = 0.7. In other words, Steven
believes that 70% of the school falls under the
category male or athlete or both. What is wrong
with Steven’s thinking?
(Try a Venn Diagram for what he says.)
Vocabulary and Notation Practice Problems pg 14
Julie was looking at some data and noticed that
25% of the school was 9th grade and that 20% of
the school was in 10th grade. She concluded that
P(9th U 10th) = 0.45. In other words Julie believes
that 45% of students are either 9th or 10th grade.
Is she correct in her thinking? Explain
(Try a Venn Diagram for what she says.)
The Addition Rule - Task - Student Council
B
C
G
F
A
D
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H
J
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P
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Q
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F = freshman
S = sophomore
B
C
J= junior
G
F
A
D
E
H
J
I
P
N
K
M
L
Q
O
R
S
T
F = freshman
S = sophomore
B
C
J= junior
G
F
A
D
E
H
J
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P
N
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M
L
Q
O
R
S
T
M = male
J= junior
B
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G
F
A
D
E
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J
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P
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N. Write a sentence or two explaining how to
calculate the probability of the union of two events.
If two events are mutually exclusive you can
calculate the probability of the union of the two
events by adding the probabilities of each
individual event, (since they do not overlap each
other.) P(1U2) = P(1) + P(2)
P1
P2
If two events are not mutually exclusive you can
still calculate the probability of the union of the
two events by adding the probabilities of each
individual event, but then you have to subtract the
probability of the intersection of the 2 events (so it
doesn’t get counted twice).
P1
P(1U2) = P(1) + P(2) - P(1
2)
P2
Homework - The Addition Rule Practice Problems
Page 21 and 22
6 problems - Use additional paper to write the
answers out if there isn’t enough room for your
writing to be clear and neat on the worksheet
itself.
Important Dates
Video Project - including one finalized storyboard per group May 13th.
Tuesday May 31st Semester 2 Final
15 iReady lessons from students who had to do the lessons.
(There are 20 - so can do extra credit)
(I think the program locks you out after a certain amount of time
in a day, so don’t leave it until the last minute to do the
lessons).