You are Here: Home >< Maths

# Justification for conditional probability. watch

1. 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 .
2. (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 .
Does this help?

Attached Images

3. (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 .
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.
4. Fantastic explanation thanks.

Is the law of total probability just an extension of this then?
5. (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

6. (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!
7. (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 . 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

8. Beautifully explained.

Thank you both of you.

I would rep but I already have too much.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 28, 2015
Today on TSR

### Struggling to get going with your revision?

Get going with the all day revision thread

### Uni strikes! How do they affect you?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

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