Download Geometry Unit 5

Geometry Unit 5
Probability and Statistics (2)
14 April 2017 - web version
Agenda 4/14/2017
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Bulletin
Arcs and Angles Homework ? turn in (p. 165 - 168)
How Random is a Coin toss?
Homework - correct homework from Wednesday (pages
1-4 of Probability and Statistics Workbook).
Homework was : Correct tonight for homework:
Probability Review Lesson 1.
Sample Space, Events and Notation
Read pages 1 and 2.
Complete the Probability Review Questions Homework Lesson 1 on pages 3 and 4.
See slides that follow to correct your work before next class.
Sample Space - set of all possible outcomes
Rolling 2 die
Sample Space - set of all possible outcomes
White
Red
1
2
3
4
5
6
1
2
3
4
5
6
Sample Space - set of all possible outcomes
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
Sample Space - compare to set notation on page 1
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
Sample Space - what notice about total outcomes?
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
Sample Space
6 x 6 = 36 total outcomes
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
Sample Space for flipping a coin one time
Using Set notation
S = {H, T}
S sample space
{ all possible outcomes }
Event - subset of the sample space
Using Set notation
S = {H, T}
S sample space
{ all possible outcomes }
Event B is the event of flipping a head
with a coin
B = {H}
Probability of an event
S = {H, T}
B = {H}
P(B) = ½
Probability of an event
S = {H, T} Possible outcomes 2
B = {H} favorable outcomes 1
P(B) = ½
P(event) = number of favorable outcomes
# of total possible outcomes
P(Sum of 7) =
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
P(Sum of 7) = 6/ 36 = ⅙
White
Red
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2,5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4,6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5,6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6,6
P(Sum of 7) = 6/ 36 = ⅙
One in six chance of rolling a
sum of seven when we roll two
dice.
P(sum of 7) = 0.16 or 17%
Probability Review Questions Homework Lesson 1
1. A box contains 4 opals, 5 garnets, and 6
pearls.
List the sample space
Below.
Sample space for which
event?
Probability Review Questions Homework Lesson 1
1. A box contains 4 opals, 5 garnets, and 6
pearls.
List the sample space
Below for selecting one
Jewel at random.
Probability Review Questions Homework Lesson 1
1. A box contains 4 opals, 5 garnets, and 6
pearls.
List the sample space below for selecting one
jewel at random.
S={
Probability Review Questions
1. A box contains 4 opals, 5 garnets, and 6
pearls.
List the sample space below for selecting one
jewel at random.
S = {O, O, O, O,
Probability Review Questions
1. A box contains 4 opals, 5 garnets, and 6
pearls.
List the sample space below for selecting one
jewel at random.
S = {O, O, O, O, G, G, G, G, G, P,P,P,P,P}
Probability Review Questions
2.A box contains 4 opals, 5 garnets, and 6 pearls.
A jewel is selected at random.
List each event as a set.
a) An Opal = {O, O, O, O}
b) Either an opal or a pearl
={O,O,O,O,P,P,P,P,P,P}
c) A garnet = { G, G, G, G, G}
d) Not a garnet = same as b).
Probability Review Questions
3. A coin is tossed, then a die is rolled. List the
sample space below
S ={H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
4. A coin is tossed, then a die is rolled. Are these
independent or dependent events? Explain.
Independent events. The outcome of tossing the
coin has no impact on the outcome when tossing
the die.
Probability Review Questions
5. A coin is tossed, then a die is rolled. Find each probability (use
sample space in question 3 above).
a) P(heads and a six) = 1/12 or 0.083 or 8.3%
b) P(tails and an even number) = 3/12 = ¼ or 0.25 or 25% {T2,
T4, T6}
c) P(heads and a number less than 3) = 2/12 = ⅙ or 0.167 0r
16.7%
d) P(tails and 3) = 1/12 or 0.83 or 8.3%
e) P(heads and a number greater than 2) = 4/12 = ⅓ or 0.33 or
33%
Probability Review Questions
6. One bag contains 3 read and 4 white balls. A second bag
contains 6 yellow and 3 green balls. One ball is drawn from each
bag. Find each probability.
a) P(red and yellow) = (3/7)x(6/9) = 2/7 or 0.286 or 28.6%
b) P(white and not green) = (4/7)x(6/9)= 8/21 or 0.38 or 38%
c) P(red and green) = (3/7)x(3/9) = 1/7 or 0.143 or 14.3%
Probability Review Questions
7. Keith makes up a deck of 40 cards. The cards are numbers
from 1 to 10 and each number has a color: orange, red, black and
blue. Keith selects 2 cards from the deck and does not replace
them. Are the events of drawing the first card and the event of
drawing the second card independent or dependent events?
Explain.
These are dependent events. Once you remove a card there are
fewer cards to choose from and so the outcome of the first event
(selecting the first card) affects the outcome of the selection for
the second card.
Probability Review Questions
8. Keith makes up a deck of 40 cards. The cards are numbers
from 1 to 10 and each number has a color: orange, red, black and
blue. Keith selects 2 cards from the deck and does not replace
them. Find the probability of each outcome:
a) P(a 5 and then a 9) = (4/40)x(4/39) = 4/390 = 2/195 or 0.01 or
1%
b) P(two 7s) = (4/40)x(3/39) = (1/10)(1/13) = 1/130 or 0.008 or
0.8%
c) P(an orange then a blue) = (10/40)(10/39) = (¼)(10/39) = 5/78
or 0.064 or 6.4%
Probability Review Questions
8. Keith makes up a deck of 40 cards. The cards are numbers
from 1 to 10 and each number has a color: orange, red, black and
blue. Keith selects 2 cards from the deck and does not replace
them. Find the probability of each outcome:
d) P(an orange 10 and then a blue 8) = (1/40)x(1/39) = 1/1560 or
0.0006 or 0.06%
e) P(7 and then a red 5) = (4/40)x(1/39) = 1/390 or 0.0026 or
0.26%
Probability Review Questions - START 4/14/2017
9. If you toss a coin six times, what is the probability of it landing
on heads every time?
Probability Review Questions - START 4/14/2017
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/ 64
Or (½)6
What are we assuming about the events?
We assuming that...
Probability Review Questions - START 4/14/2017
9. If you toss a coin six times, what is the probability of it landing
on heads every time?
We assuming that each time we toss a coin
the outcomes are independent events, in
other words that the probability of the coin
landing on heads one time has no effect on
the probability of it landing on heads the
next time.
Have you ever wondered if it matters which side is
facing up when you flip a coin?
This scientist did, let’s watch what he did to investigate the
question.
https://www.youtube.com/watch?v=AYnJv68T3MM&list=PLsJTOc1vcSV63J5CB6fdTjoTwhCNkldOD&index=12
Have you ever wondered if it matters which side is
facing up when you flip a coin?
This scientist did, let’s watch what he did to investigate the
question.
https://www.youtube.com/watch?v=AYnJv68T3MM&list=PLsJTOc1vcSV63J5CB6fdTjoTwhCNkldOD&index=12
Key Question: Does it matter which way up the coin is at the
start?
Your initial prediction and explanation...
Key Question: Does it matter which way up the coin is at
the start?
Your initial prediction and explanation…
Will the outcome of tossing a coin be independent of the face
that is up before the toss? Explain why you think that.
Instructions.
Group 1. Always has the coin heads up before flipping.
Work in pairs. One person start with your coin heads up and
flip it. Catch the coin and the partner records whether it is a
head or a tail. Repeat until you have a set of 50 results. Then
switch jobs so the recorder gets to flip and the flipper records
to generate another set of 50 results.
Group 2. Always has the coin tails up before flipping.
Instructions. Try to make the coin “flip” - only count
ones you catch. Stop at 50 catches.
Group 1. Always has the coin heads up before flipping.
Recorder makes tally marks on your paper as you flip.
You make tally marks on their paper as they flip.
Group 2. Always has the coin tails up before flipping.
Recorder makes tally marks on your paper as you flip.
You make tally marks on their paper as they flip.
Class data collection:
https://docs.google.com/spreadsheets/d/1fytMQIeLzWNeY356tC1OsZpMIx3cGiyv
22_sZkbj5dg/edit#gid=1477861470
Enter your data into the spreadsheet - it will total the values
for us so we can fill in the two-way table on the back of your
worksheet.
Class Data Analysis
Class Data for
all groups that Ended heads
caught coins
Ended tails
Totals
421
379
800
390
410
800
811
789
1600
Started heads
Started tails
Totals