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Probability

1.Events X and Y are mutually exclusive.Suppose P(A)=0.30 and P(B)=0.20 .
   What is the probability that A or B occurring? 
 
2.Suppose P(A)=0.04 and P(B/A)=0.30.
What is the joint probability of A and B?
 
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1 Answer

1.
Here,
       P(A) = 0.3
       P(B) = 0.2
If events A and B are mutually exclusive, then there is no common element in A and B.
So, A ∩ B = Ø = null set
Therefore, P(A ∩ B) = 0
P(either A or B occurring) = P(A ∪ B)
By addition theorem of probability,
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
             = 0.30 + 0.20 - 0
             = 0.50
Hence, the probability that A or B occurring is 0.50
 
2.
Here,
        P(A) = 0.04
        P(B/A) = 0.30
We want to find the joint probability of A and B that is P(A ∩ B)=?
We know,
             P(B/A) = P(A ∩ B)/P(A)
         or P(A ∩ B) = P(A)*P(B/A)
                          = 0.04*0.30
                          = 0.12
Hence, the joint probability of A and B is 0.12

Comments

Hello Ken please check problem 2. There was a mistake as I put P(A ∩ B) in place of P(A ∩ B). I've just updated the solution. Please check. Thank you
I mean P(A ∪ B) in place of P(A ∩ B).......lol
In 1, the givens are that X and Y are mutually exclusive. But this is irrelevant to events A & B; they may or may not be mutually exclusive!  I think you made an unwarranted assumption.