Let A and B be two events such that PA 6 and PB 8 Which ad

Let A and B be two events such that P(A) = .6 and P(B) = .8. Which additional information

will be sufficient in order to find P(A B)? There is no need to do any calculations!

(a) knowing that A and B are independent

(b) knowing that P(A|B) = .3

(c) knowing that A and B are disjoint

(d) knowing that P(A B) = .7

(e) any one of the above options would be sufficient.

Solution

IT IS

OPTION E: any one of the above options would be sufficient.
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This is so because if they are independent, then we know

P(A n B) = P(A) P(B). [a]

Also, we know

P(A|B) = P(A n B)/P(B) [b]

If they are disjoint,

P(A n B) = 0 [c]

Also, we know

P(A U B) = P(A) + P(B) - P(A n B). [d]

So, all of these are sufficient.