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# S1 Probability help Watch

1. Events A and B are independent with P(A) = 1/4 and P(AUB) = 2/3
Find:
b) P(B)
Independent so P(A)P(B) = P(ANB) therefore = 1/4P(B)
So P(A) + P(B) - P(ANB) = P(AUB)
Therefore 1/4 + 3/4P(B) = 2/3
Therefore 2/3 - 1/4 = 5/12
P(B) = 5/12 over 3/4 = 5/9 right??
c) P(A'|B) = ??
d) P(B'|A) = ??
2. Wait it's 5/12 and 1/9 respectively right??
3. (Original post by AlphaArgonian)
Events A and B are independent with P(A) = 1/4 and P(AUB) = 2/3
Find:
b) P(B)
Independent so P(A)P(B) = P(ANB) therefore = 1/4P(B)
So P(A) + P(B) - P(ANB) = P(AUB)
Therefore 1/4 + 3/4P(B) = 2/3
Therefore 2/3 - 1/4 = 5/12
P(B) = 5/12 over 3/4 = 5/9 right??
If you have 2/3 = 1/4 * P(B) - then how can you find P(B)?
4. (Original post by Zacken)
If you have 2/3 = 1/4 * P(B) - then how can you find P(B)?
Divide both sides by 1/4
Wait why?
5. (Original post by AlphaArgonian)
Divide both sides by 1/4
Wait why?
6. Oh, and: moved to maths.
7. (Original post by Zacken)
Uhhh I get 8/3 from that
8. (Original post by AlphaArgonian)
Divide both sides by 1/4
Wait why?
If then: , in this case, .
9. (Original post by AlphaArgonian)
Uhhh I gett 8/3 from that
10. (Original post by Zacken)
Haha, that's fine I'll probably do that in the real exam this year
11. (Original post by AlphaArgonian)
Events A and B are independent with P(A) = 1/4 and P(AUB) = 2/3
Find:
b) P(B)
Independent so P(A)P(B) = P(ANB) therefore = 1/4P(B)
So P(A) + P(B) - P(ANB) = P(AUB)
Therefore 1/4 + 3/4P(B) = 2/3
Therefore 2/3 - 1/4 = 5/12
P(B) = 5/12 over 3/4 = 5/9 right??
c) P(A'|B) = ??
d) P(B'|A) = ??

Yeah, you get 5/9. That's correct.

For the next part, try looking at the conditional probability formula and recall how you can write P(A' if you know P(A).
12. (Original post by Zacken)
Yeah, you get 5/9. That's correct.

For the next part, try looking at the conditional probability formula and recall how you can write P(A' if you know P(A).
Ah thanks
1-P(A)?
13. (Original post by AlphaArgonian)
Ah thanks
1-P(A)?
Yep.
14. (Original post by Zacken)
Yep.
Cheers
15. (Original post by Zacken)
Yeah, you get 5/9. That's correct.

For the next part, try looking at the conditional probability formula and recall how you can write P(A' if you know P(A).
(Original post by AlphaArgonian)
Cheers
.
Also, if A and B are independent, A' and B are also independent, so P(A'|B) = P(A')

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Updated: February 17, 2016
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