Upload
lucine
View
154
Download
1
Embed Size (px)
DESCRIPTION
Conditional Probability in Venn Diagrams. Slideshow 59, Mathematics Mr Richard Sasaki, Room 307. Recall how to insert data into Venn Diagrams Find probabilities in Venn Diagrams and understand how conditions affect them. Objectives. - PowerPoint PPT Presentation
Citation preview
Conditional Probability in Venn Diagrams
Slideshow 59, MathematicsMr Richard Sasaki, Room 307
Objectives
• Learn to draw Venn Diagrams for Four Sets• Review and picture sections in simple Venn
Diagrams (two sets)• Understand Conditional Probability in Venn
Diagrams
4 Set Venn Diagrams
A regular Venn Diagram must cover all options.It cannot be made simply with just circles.
This pattern does not cover Red and Green or Yellow and Blue.In fact, to cover all possibilities, there must be sections. (including the outside).
16
4 Set Venn DiagramsSome solutions are…
This one has 11 sets… (It was discovered 3 years ago.)
What makes this special is that it’s symmetrical.
Introduction
We know how to use Venn Diagrams now (this is our third slideshow on Venn Diagrams).
Set A Set B
𝐴∩𝐵 ′𝐴∩𝐵𝐴 ′ ∩𝐵
𝐴 ′ ∩𝐵 ′
The total number of values in this diagram is the number of entries surveyed.
Number of Entries =𝐴∩𝐵′+ 𝐴∩𝐵+𝐴′∩𝐵+ 𝐴 ′ ∩𝐵 ′𝑃 (𝐴∩𝐵 ′)+𝑃 ( 𝐴∩𝐵 )+𝑃 (𝐴′∩𝐵 )+𝑃 ( 𝐴′∩𝐵′ )=¿1
ProbabilitiesIf we choose one of the entries surveyed at random, we can find the probability of it being in its given category.
Set A Set B
1371911
ExampleTotal # of entries: 50
𝑃 ( 𝐴)=¿2050𝑃 (𝐵 ′ )=¿2450𝑃 (𝐴∩𝐵)=¿750
𝑃 (𝐴∩𝐵 ′ )=¿1350𝑃 (𝐴 ′ ∩𝐵 ′)=¿1150𝑃 (𝐴∪𝐵)=¿3950Note: . 𝑃 (𝐴 ′ ∩𝐵 ′)
Shading Exercise
Firstly I’d like us to do a shading in exercise. Shade in the areas mentioned on your worksheet.Answers
Conditional Probability
Conditional probability refers to…The likelihood of something happening changing, depending on whether something else happens or not. (For example:
)If A happens, P(B) is lower
than when A doesn’t happen.When in daily life might this happen?Wearing Glasses and taking an eye exam
Passing an exam after studying for hours
Being able to kiss a girl after eating garlic
Conditional Probability
For this we use given that which has the ‘|’ symbol. What does mean?It means, assuming A is true, find the chance of B being true.
Set A Set B2435
𝑃 (𝐵|𝐴 )=¿37which is different from . 814
Note: Most of your examples would have been two events happening in turn (like with tree diagrams). But Venn diagrams show relationships as a whole, ignoring time.
How about for the Venn diagram on the right?
Conditional Probability
Set A Set B
914423
Example
Total # of entries: 50
𝑃 ( 𝐴)=¿2350𝑃 (𝐵∨𝐴 )=¿1423𝑃 ( 𝐴∨𝐵 )=¿1418𝑃 ( 𝐴∨𝐵 ′ )=¿932
Try the ActivExpression exercise!
A group of 50 people are asked whether they wear glasses and whether they wear contact lenses. 23 people wear glasses (Set A), 18 wear contacts (Set B) and 14 use both.
If picked randomly, find…
6401440526513813
Set A Set B
29301328
100𝑃 (𝐴∩𝐵 ′)= 30
100
𝑃 (𝐵∨𝐴 )=2959
(A)
(A)
Set A Set B
Set C