Math Is Fun Forum

mathwonka

Guest

S1 notation help?

hello,

again i am stuck on a question in an S1 past paper.

"3) The events A and B are such that

P(A) = 0.2 and P(A U B) = 0.6

Find

(a) P(A' n B')
(b) P(A' n B)

Given that events A and B are independent, find

(c) P(B)
(d) P(A' U B')

I know that "n" means and, and "U" means or.

i thought that P(B) should be 0.4 because its saying the probability of A OR B occurring so 0.2 + B = 0.6 so B = 0.4. the mark scheme says this is wrong...

can anyone tell me how to do this?

also, i can't do any of the other questions, because i don't know what A' means, or B'...what does the dash/apostrophe mean?

mathwonka

Guest

Re: S1 notation help?

i take it A' means NOT A?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: S1 notation help?

hi mathwonka

Yes A'  means not in A

I've put a (Venn) diagram below that shows the four spaces, in A but not B; in both, in B but not A; not in either.

You know that P(A) = 0.2 which includes P(A n B') and P(A n B)

If P(A u B) = 0.6 then taking out the bits in A leaves P(B n A') = 0.4

So P(A' n B') = 0.4 also ( = 1 - 0.2 - 0.4)

Now if the events are independant P(A when B is known to have occurred) = P(A)

So let P(A n B) = x  => P(B) = x + 0.4

So P(A when B is known to have occurred) = x / (x + 0.4)

so x/(x + 0.4) = 0.2  => x = 0.1

So you can now fill in the Ps for all four spaces and complete the question.

Bob

Last edited by Bob (2011-02-13 08:52:18)

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