S1 - probabilities Watch

gooner88
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#1
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#1
hi, im having trouble with this question.

Given that
P(A) = 5/16, P(B) = 1/2 , P(A | B) = 1/4

find

a. p(AnB) - this one i find easy p(AnB) = p(A|B) x p(B)
b. P(B′|A)
c. P(A′∪B)

part b and c i don't understand how to do.
could someone help me plz? thanks
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M1N1
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OK, I'm doing S1 tomorrow, but my class only started getting taught it in April, so I'm not too confident on this. But I think I've got b):

Firstly, draw a Venn Diagram with all of the numbers filled in, and then its easier to see what's going on. You can then see that P(B'nA) is 3/16 (with a bit of number manipulation, I hope thats right). You can also see that, as it says in the question, P(A) = 5/16. Therefore the P(B'|A) = 3/5.

I can't see what the thing between the A' and the B in part c) is,

Hope this helped, it certainly helped me,

PK
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Paulus
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I find that its always best to draw a Venn diagram.
You will have 2 circles overlapping
(because P(A) x P(B) does not equal P(AnB), because they are not independant).

In the A circle you will have 3/16 because P(A) - P(AnB) = 3/16
In the middle you will have P(AnB) = 2/16
In the B circle you will have 6/16 because P(B) - P(AnB) = 6/16
Outside you will have 5/16 because 1 -(sum of all other probabilities) = 5/16

For part b, you can see from the Venn diagram that P(A) = 5/16 and that the section that is NOT B is 3/16. So:
(3/16) / (5/16) = 0.6
Alternatively:
3/5 = 0.6

For part c, I assume that is P(A'uB).
On the Venn diagram, the P(A') includes everything outside the A circle and the "uB" adds the middle section (AnB). From this you can see that the answer is 2/16 + 6/16 + 5/16 = 13/16.

Please note that this is just my way of doing it and I also often make stupid mistakes so dont assume that its correct.
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hotfreezer
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P(A′∪B) = probability of either A' or B or both:

probability of A' n B' = 5/16

probability of B = 1/2

P(A'UB) = 5/16 + 1/2 = 13/16
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suneilr
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P(A'UB) = P(A') + P(B) - P(A'nB)
= 11/16 + 4/8 - 3/8
= 13/16

I find that using the formula is the easiest method.
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gooner88
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so, for part b p(B' | A) = p(B' n A) / p(A) ???

and i get part C, the venn diagram makes it much easier. thanks
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Neo1
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(Original post by suneilr)
P(A'UB) = P(A') + P(B) - P(A'nB)
= 11/16 + 4/8 - 3/8
= 13/16

I find that using the formula is the easiest method.

Where did you get the 4/8 from P(B)...shouldnt it be 1/2 ?


Thanks
From John
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suneilr
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(Original post by Neo1)
Where did you get the 4/8 from P(B)...shouldnt it be 1/2 ?


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From John
4/8 is 1/2 :rolleyes:
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