S1 - Conditional Probabilty PLEASE HELP!!

I understand everything about all of my subjects even some of the hardest concepts but for some reason I just can not get conditional probability or just probabilty at all!
The text book I have conflicts with the revision guide I have which conflicts with the exam papers! It's ridiculous and I just don't get it!

I know the basic concepts of probabilty, i.e:

probabilty of rolling a 6 and a 2 = 1/6 x 1/6
6 or a 2 = 1/6 + 1/6

I get all that but all this sample space, sets, A given B, I mean what the hell can someone please just give me a brief overveiw, hopefully it won't take up too much of your time (don't spend hours typing something out!!)

Any half-decent help will be appreciated!

Reply 1

Glutamic Acid

17

Conditional probability was my weak point...

but say you want to work out A given B, it basically means that you want to work out the total probability of events where A and B both occur, divided by the probability that B has occurred.

I'm sure someone will else will explain this clearly.

Reply 2

Blundell

OP

1

Glutamic Acid

Conditional probability was my weak point...

but say you want to work out A given B, it basically means that you want to work out the total probability of events where A and B both occur, divided by the probability that B has occurred.

I'm sure someone will else will explain this clearly.

I get that P(A|B) is just P(A) given that P(B) has already happened but when it comes to the formulas it's just... ARRRGH, I HATE STATS!!!

Reply 3

Glutamic Acid

17

Blundell

I get that P(A|B) is just P(A) given that P(B) has already happened but when it comes to the formulas it's just... ARRRGH, I HATE STATS!!!

Yeah, it's [P(A and B)]/P(B), so the probability of P(A) and P(B) occurring, divided by the probability that P(B) has occurred.

What exam board are you on? For OCR you do not need to be aware of the formula, merely be aware of what conditional probability is.

Reply 4

Kyalimers

21

\displaystyle P(A|B) = \frac{P(A\cap B)}{P(B)}

Reply 5

Daniel Freedman

7

@ Sohanshah: I think \cap is the code you're looking for.

Are you comfortable with the idea of probability trees? It helps to look at conditional probablility that way. If event A happens first, followed by event B, then the probability of A and B happening (written as

P(A \cap B)

) is going to be the product of the probability of the first branch (i.e. A occuring) and the probability of the B branch that comes off A. This B branch, that occurs after A, is conditional on A occuring. This is written as

P(B|A)

- said as "the probability of B given A".

The whole "set" idea is best understood with a Venn Diagram.

P(A \cap B)

- said as the "intersection of A and B" - is the little section that A and B share (i.e they both occur).

P( A \cup B)

- said as the "union of A and B" - is the whole area contained in A and B, including that little bit in the middle

P(A \cap B)

. From this you should be able to see that

P(A \cup B) = P(A) + P(B) - P(A \cap B)

. (that is if they are not mutually exclusive i.e. they have that overlap to take away).

Reply 6

Kyalimers

21

Daniel Freedman

I think \cap is the code you're looking for.

Thank you.

Reply 7

Blundell

OP

1

I'm OCR but you do need the formula, i.e. I was doing a question today that required a formula that was not even mentioned in the text book! I had to look it up in the formula book instead...

I know that P(A|B) = P(A and B) / P(B) but that just = P(B) x P(A|B) / P(B) = P(A|B)!!

The formula really isn't helpful and is just common sense for most questions.

Reply 8

Glutamic Acid

17

You can use a tree diagram.
Total the probabilities where both A and B have occurred.
Total the probabilities where B has occurred.
And divide the first by the second.

Do you have any specific questions? It may be easier to go through it that way.

Reply 9

Adjective

12

A more intuitive way of looking at

\displaystyle \frac {P(A \cap B)}{P(B)}

(for me, anyway) is to draw a tree diagram with the primary branches being A and A', and the secondary branches being B and B' - and expanding the above formula to:

\displaystyle P(A|B) = \frac {P(A \cap B)}{P(B)} = \frac {P(B|A) \, . \, P(A)}{P(B|A) \, . \, P(A) + P(B|A') \, . \, P(A')}

S1 - Conditional Probabilty PLEASE HELP!!

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