conditional probability - gorski compscigorskicompsci.ca › mdm4u › 1_prob ›...
TRANSCRIPT
![Page 1: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/1.jpg)
Conditional ProbabilityGiven that…..
A.1.6 determine whether two events are independent or dependent and whether one event is conditional on another event, and solve
related probability problems [e.g., calculate P(A and B), P(A or B), P(A given B)] using a variety of strategies (e.g., tree diagrams, lists, formulas)
![Page 2: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/2.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
![Page 3: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/3.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
Draw the Venn
Diagram.
![Page 4: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/4.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
NewMedication
Slept Draw the
Venn Diagram.
![Page 5: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/5.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
NewMedication
Slept
3515 20
20
Draw the Venn
Diagram.
![Page 6: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/6.jpg)
NewMedication
Slept
3515 20
20
Given that they slept well, what was the probability they had medication?
![Page 7: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/7.jpg)
NewMedication
Slept
3515 20
20
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
![Page 8: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/8.jpg)
NewMedication
Slept
3515 20
20
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
Given that they slept well, what was the probability they had a placebo?
![Page 9: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/9.jpg)
NewMedication
Slept
3515 20
20
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
Given that they slept well, what was the probability they had a placebo?
=20
55= 36.3%
![Page 10: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/10.jpg)
NewMedication
Slept
3515 20
20
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
Given that they slept well, what was the probability they had a placebo?
=20
55= 36.3%
What do we know about the
medication? Does it work?
![Page 11: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/11.jpg)
NewMedication
Slept
3515 20
20
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
Given that they slept well, what was the probability they had a placebo?
=20
55= 36.3%
What do we know about the
medication? Does it work?
Because the people with the medication were more likely to sleep well, we can tell that the medication works better than a placebo.
![Page 12: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/12.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
Placebo
Med
![Page 13: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/13.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
Slept
Slept
Didn’t
Didn’tPlacebo
Med
![Page 14: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/14.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
Slept
Slept
Didn’t
Didn’tPlacebo
Med
55
100
45
100
![Page 15: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/15.jpg)
A randomized study of 100 people was done for a new sleeping pill.
Slept Well Did not sleep well
Placebo 35 20
New Medication 30 15
Slept
Slept
Didn’t
Didn’tPlacebo
Med
55
100
45
100
35
55
20
55
30
45
15
45
=7
20
=4
20
=6
20
=3
20
![Page 16: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/16.jpg)
Slept
Slept
Didn’t
Didn’tPlacebo
Med
55
100
45
100
35
55
20
55
30
45
15
45
=35
55
Given that they slept well, what was the probability they had medication?
= 63.6%
Given that they slept well, what was the probability they had a placebo?
=20
55= 36.3%
![Page 17: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/17.jpg)
NewMedication
Slept
3515 20
20
Slept
Slept
Didn’t
Didn’tPlacebo
Med
55
100
45
100
35
55
20
55
30
45
15
45
Conditional Probability is like “Pruning a Tree”
Conditional Probability is like “Zooming in on A
Venn Diagram”
![Page 18: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/18.jpg)
Flash Cards 80% on Test
455 10
40
Given that you used flash cards, what is the probability you got 80% on the test?
=45
50= 90%
Given that you used flash cards, what is the probability you didn’t get 80% on the test?
=5
50= 10%
![Page 19: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/19.jpg)
Flash Cards 80% on Test
455 10
40
Given that you got 80% on the test, what is the probability you used flash cards?
=45
55= 82%
Given that you got 80% on the test, what is the probability you didn’t use flash cards?
=10
55= 18%
![Page 20: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/20.jpg)
𝑃(𝐴|𝐵) =𝑃(𝐴𝐵)
𝑃(𝐵)A AB B
![Page 21: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/21.jpg)
![Page 22: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/22.jpg)
![Page 23: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/23.jpg)
![Page 24: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/24.jpg)
![Page 25: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/25.jpg)
![Page 26: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/26.jpg)
![Page 27: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/27.jpg)
(a) Student has a chocolate bar poor hearing(b) A worker is well trained meets the production
quota(c) A dog Likes running Has a name that starts
with “M”(d) A person is Late Had trouble sleeping(e) Playing a game Draw an Ace of
SpadesRoll a pair of 6’s with dice
(f) A person is left handed has blonde hair(g) A person plays squash tennis
Identify as independent or dependent.
![Page 28: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/28.jpg)
𝑃(𝐴𝐵) = 𝑃(𝐴) × 𝑃(𝐵)
If independent:
![Page 29: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/29.jpg)
A coin and die are tossed. Determine the probability of getting a head and a 3 without using a tree diagram.
𝑃(𝐻𝑅𝑜𝑙𝑙 3) = 𝑃(𝐻) × 𝑃(𝑅𝑜𝑙𝑙 3)
=1
2×1
6
=1
12
![Page 30: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/30.jpg)
![Page 31: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/31.jpg)
![Page 32: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/32.jpg)
We know a lot of formulas with AND:
Mutually Exclusive?
Additive Principle?
Independent?
Conditional probability?
![Page 33: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/33.jpg)
![Page 34: Conditional Probability - Gorski CompScigorskicompsci.ca › MDM4U › 1_Prob › ppt6_ConditionalProbability.pdf · Conditional Probability Given that….. A.1.6 determine whether](https://reader033.vdocument.in/reader033/viewer/2022053008/5f0b872b7e708231d430f5c9/html5/thumbnails/34.jpg)