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# Probability S1 Help!! Watch

1. The question states:

Two events R and S are independant. P(R|S) = 3/4 AND P(S) = P(S'nR'). By letting x equal P(S) and forming an equation for x, or otherwise, find:

a) P(S)
b) P(S'UR)
c) Write down P(S|R)

There's obviously some link between P(S) = P(S'nR') and R and S's indepedence but I'm not seeing it.

Help.

Socratic method preferred.
2. (Original post by Mambo No. 5)
...

1) What's P(R)?

2) If S and R are independent, what can you can about S' and R'?
3. (Original post by ghostwalker)

1) What's P(R)?

2) If S and R are independent, what can you can about S' and R'?
1) ?

2) Well if they're independent, then we know that P(S) x P(R) = P(SnR)
4. (Original post by ghostwalker)

1) What's P(R)?

2) If S and R are independent, what can you can about S' and R'?
I just put:

P(R) x P(S)/P(S) = 3/4

Cancelling out P(S) means P(R) = 3/4 ?
5. (Original post by Mambo No. 5)
1) ?
You're told P(R|S) and that R and S are independent. Use the definition of independence.

2) Well if they're independent, then we know that P(S) x P(R) = P(SnR)
What about S' and R' ?
6. (Original post by Mambo No. 5)
I just put

P(R) x P(S)/P(S) = 3/4

Cancelling out P(S) means P(R) = 3/4 ?
Yes.
7. (Original post by ghostwalker)
Yes.
So if P(R) is equal to 3/4

...How is this fact used with P(S'nR') to find P(S)?

I know P(R') = 1/4 if that's relevant.
8. Bump.
9. Bump.
10. Bump.
11. (Original post by Mambo No. 5)
So if P(R) is equal to 3/4

...How is this fact used with P(S'nR') to find P(S)?

I know P(R') = 1/4 if that's relevant.
You keep ignoring my question about R' and S'; so much for Socrates.

P(R'nS') = P(R')P(S') since R and S are independent, then so are R' and S'. Using that you can formulate your equatiion in "x" as per the original question.
12. (Original post by ghostwalker)
You keep ignoring my question about R' and S'; so much for Socrates.

P(R'nS') = P(R')P(S') since R and S are independent, then so are R' and S'. Using that you can formulate your equatiion in "x" as per the original question.
So far I've got:

P(R|S) = 3/4
P(R) = 3/4
P(R') = 1/4

P(SnR) = P(S) X P(R)
P(S'nR') = P(S') X P(R')

P(SnR) = P(S) X 3/4
P(S'nR')= P(S') X 1/4

P(R'|S') = 1/4

(Mind Block)
13. (Original post by Mambo No. 5)
So far I've got:

P(R|S) = 3/4
P(R) = 3/4
P(R') = 1/4

P(SnR) = P(S) X P(R)
P(S'nR') = P(S') X P(R')

P(SnR) = P(S) X 3/4
P(S'nR')= P(S') X 1/4

P(R'|S') = 1/4

(Mind Block)
Use the method they suggest in the question on the equation P(S) = P(S'nR'). You've worked out most of the stuff you need for it.
14. (Original post by ghostwalker)
Use the method they suggest in the question on the equation P(S) = P(S'nR'). You've worked out most of the stuff you need for it.
That's (^^^) the part I seem to be having the most trouble with.

15. (Original post by Mambo No. 5)
That's (^^^) the part I seem to be having the most trouble with.

The only bit you are missing is P(S') = 1- P(S)

You now have everything you need to make the equation using the substitution they suggest.

Post working if you're still having problems.

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