Q. 1 B

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A B) =0.35. Find (i) P(A B), (ii) (iii) (iv)

Answer :

Given A and B are two events


And, P(A) = 0.54 P(B) = 0.69 P(A B) = 0.35


By definition of P(A or B) under axiomatic approach we know that:


P(A B) = P(A) + P(B) – P(A B)


We have to find-


i) P(A B) = P(A) + P(B) – P(A B)


= 0.54 + 0.69 – 0.35 = 0.88


ii) P(A’ B) = P(A B)’ {using De Morgan’s Law}


P(A’ B) = 1 P(A B) = 1 – 0.88 = 0.12


iii) P(A B’) = This indicates only the part which is common with A and not B This indicates only A.


P(only A) = P(A) – P(A B)


P(A B’) = P(A) - P(A B) = 0.54 – 0.35 = 0.19


iv) P(A’ B) = This indicates only the part which is common with B and not A This indicates only B.


P(only B) = P(B) – P(A B)


P(A’ B) = P(B) – P(A B) = 0.69 – 0.35 = 0.34


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