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venn diagram help: P(A n B) and P(A) times P(B)

basicallyy in a venn digram if i have circle A and cirlcle B and they over lap calling the middle bit P

if the question states P(A n B) = that could be the value of P right ?

but how do you know not to do P(A)*P(B) ?

[btw not too sure if the overlap is U or n but either way correct me]
hopefully yous get my point
please help

Reply 1

bcrazy

Original post by Tishax2

Firstly, you are correct in thinking that the overlap is n.
Secondly, yes, P(A n B) would be the value in the overlap (assuming these values are probabilities!)
At times you would also have a choice of doing P(A)*P(B) but this is only if A and B are independent (i.e. A is just as likely to happen whether or not B happens).

For example, if A represented the event of rolling an odd number on a die and B represented the event of flipping a head on a coin then you could do P(A)*P(B) (although this would give you the same answer as the overlap anyway).

If A represented the event of rolling an odd number on a die and B represented the event of rolling a prime number on the same die then one happening effects the other and you would not be able to do P(A)*P(B).