Turn on thread page Beta
    • Thread Starter
    Offline

    13
    ReputationRep:
    Could someone clarify what i can do to simplify compliments in event probability?

    I know for certain that:

    P(E^c)=1-P(E)

    Could i do anything similar with:

    P(E^{c} \cup F^{c})

    or

    P(E^{c} \cup F)

    or

    P(E \cup F^{c})

    And also with the above 3 examples but using \cap or | instead of \cup
    Offline

    12
    ReputationRep:
    Have you heard of De Morgan's Laws?
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by GHOSH-5)
    Have you heard of De Morgan's Laws?
    I have actually, and now i remember, it does explain how to simplify when both events are compliments, but what when only one of the events in the bracket is a compliment? And how would this work for something like
    P(E|F^c)?
    Offline

    12
    ReputationRep:
    (Original post by nugiboy)
    I have actually, and now i remember, it does explain how to simplify when both events are compliments, but what when only one of the events in the bracket is a compliment? And how would this work for something like
    P(E|F^c)?
    If only one is a compliment, then for example, you can do the folllowing:

     P(E^c \cap F) : Let  F^c = D \iff F = D^c . Hence by De Morgan's Laws:  P(E^c \cap D^c) = 1 - P(E \cup D) = 1 - P(E \cup F^c) .

    For  P(E|F^c) = \dfrac{P(E \cap F^c)}{P(F^c)} = \dfrac{1 - P(E^c \cup F)}{1 - P(F)} , due to the previous paragraph.
    • Thread Starter
    Offline

    13
    ReputationRep:
    Thanks! That pretty much makes sense.
 
 
 
Poll
Which accompaniment is best?
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.