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S1 probability watch

1. I haven't done any S1 style probability since January of the lower 6th, so to say i'm rusty is an understatement. Managed to remember enough to be able to work through the other questions in this practise paper but can't for the life of me do this one:

The events A and B are such that

P(A) = 0.41 P(A n B') = 0.25 and P(A U B) = 0.52

By using a venn diagram or otherwise find
i) P(A' n B')
ii) P(A n B)
iii) P(B)

2. if you have the formulas to work out certain probabilities, you can draw your venn diagrams to help you out

P(A intersect B)= P(A) +P(B) -P(A U B) - i think thats the one, lol im doin S1 this may too
3. Read the formulas, and draw a venn diagram. For this I would draw a diagram and it all becomes apparent;

i) 1-0.52 = 0.48

ii)0.16

iii)0.27

P(A U B) = P(A) + P(B) - P(A U B)

P(A/B) = P(A n B) / P(B)
4. (Original post by Pythag)
Read the formulas, and draw a venn diagram. For this I would draw a diagram and it all becomes apparent;

i) 1-0.52 = 0.48

ii)0.16

iii)0.27

P(A U B) = P(A) + P(B) - P(A U B)

P(A/B) = P(A n B) / P(B)
I understand part i now, but can you explain ii and iii? I'm still really at a loss, cause as far as I can see i don't have enough to be able to work them out yet...
5. (Original post by CharleyChester)
I understand part i now, but can you explain ii and iii? I'm still really at a loss, cause as far as I can see i don't have enough to be able to work them out yet...
ii) P(A n B) is the centre region in the venn diagram where P(A) and P(B) overlap. You can get this through the diagram as we already know P(A) 0.41 and P(A n B') 0.25. P(A n B') means anything JUST in A, not in B, so it does not include the middle overlap section. So, by P(A) - P(A n B') we can get the middle overlap, 0.41 - 0.25 = 0.16.

Not needed in this question but for future reference, if the question states that P(A) and P(B) are independent, this formula applies if you need to find out P(A n B) or if you need to prove they are in fact independent:

P(A) . P(B) = P(A n B).

iii) P(B) can be found as we know everything in the circular regions of the diagram (JUST A, the middle BOTH A and B, and JUST B) add up to 0.52. P(A U B) means A or B or both. So, 0.52 - JUST A which is 0.25 = 0.27.

Draw a diagram of all this and it will be clearer than any words could describe.

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Updated: March 24, 2011
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