Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    9
    ReputationRep:
    I see how you can use the formula for conditional probability to prove Bayes theorem but how do yet get to the formula for conditional probability can anyone explain in an intuitive way why it should be the case that \displaystyle P(A|B)=\frac{P (A \cap B)}{P(B)}.
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by poorform)
    I see how you can use the formula for conditional probability to prove Bayes theorem but how do yet get to the formula for conditional probability can anyone explain in an intuitive way why it should be the case that \displaystyle P(A|B)=\frac{P (A \cap B)}{P(B)}.
    Does this help?

    Attached Images
     
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by poorform)
    I see how you can use the formula for conditional probability to prove Bayes theorem but how do yet get to the formula for conditional probability can anyone explain in an intuitive way why it should be the case that \displaystyle P(A|B)=\frac{P (A \cap B)}{P(B)}.
    An example that you can use with Smaug's diagram:

    There are 50 children in a class, 30 girls and 20 boys. Out of all the girls, 5 of them play the violin.

    Given that a child is a girl, what is the probability that they play violin?

    The initial sample space (children that we are interested in) is 50. When we assume that the child is a girl, the sample space reduces to 30. This is shown in the diagram when the two circles become one circle.

    The number of children that are girls and play the violin is 5 (the shaded area in the diagram). And the number of girls in total is 30. So the conditional probability is 5/30.
    • Thread Starter
    Offline

    9
    ReputationRep:
    Fantastic explanation thanks.

    Is the law of total probability just an extension of this then?
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by Smaug123)
    Does this help?
    Yes that was great?

    Any chance you could help me interpret this I just don't really see where it comes from?

    thank you for helping.

    Attached Images
     
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by poorform)
    Yes that was great?

    Any chance you could help me interpret this I just don't really see where it comes from?

    thank you for helping.

    Think back to when you used probability trees at GCSE and when you would multiply along the branches and add vertically across the branches.

    http://www.vitutor.com/statistics/pr...obability.html

    Maybe Smaug will provide you with a nice Venn Diagram illustration when he's next online!
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by poorform)
    Yes that was great?

    Any chance you could help me interpret this I just don't really see where it comes from?

    thank you for helping.

    Recall that \mathbb{P}(B \vert A_1) \mathbb{P}(A_1) = \mathbb{P}(B \cap A_1). Hence what the first equality is saying, if we interpret "probability" as "area on a Venn diagram", is simply "the area of B is the sum of the areas of B intersected with each of the covering sets".

    Attached Images
     
    • Thread Starter
    Offline

    9
    ReputationRep:
    Beautifully explained.

    Thank you both of you.

    I would rep but I already have too much.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.