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yet more probability

i refuse to learn the relationships between these probability things, and instead just try to make sense of things in my head. Well, this is a little bit complicated for my small brain, so i hand it over to you...

the events A and B are such that

P(A) = 1/2
P(A|B') = 2/3
P(A|B) = 3/7

find P(A n B)

Reply 1

username9303

p(a|b)= P(A n B) / p (B) i think - its the conditional probability rule - you can use that, or alternately draw a venn diagram.

ollie :biggrin:

Reply 2

Chewwy

olliemccowan

p(a|b)= P(A n B) / p (B) i think - its the conditional probability rule - you can use that, or alternately draw a venn diagram.

ollie :biggrin:

but i don't know P(B) :confused:

Reply 3

username9303

no you can work out the p(B) using that formula, then use that to figure out p (A n B) i guess. i'm gonna have a go lol.

Reply 4

username9303

rite i think the answer is p(AnB) is 42/161, workings to follow.

Reply 5

username9303

retract that, error in workings :frown:

sorry.

Reply 6

username9303

i'll leave it to someone else, because i'm fed up with it already lol.

ollie :biggrin:

Reply 7

Chewwy

olliemccowan

i'll leave it to someone else, because i'm fed up with it already lol.

ollie :biggrin:

lol. anyone?

Reply 8

Supermerp

P(A) = P(A n B) + P(A n B')

P(A n B) = P(A|B)P(B)

So: P(A) = P(A|B)P(B) + P(A|B')P(B') = P(A|B)P(B) + P(A|B')(1 - P(B))

Substituting in the numbers we know you get
1/2 = 3/7 * P(B) + 2/3 - 2/3 * P(B)

And then you rearrange things to get B = 7/10 and then you use P(A n B) = P(A|B)P(B) to get the answer as 3/10