Q. 255.0( 1 Vote )

Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are:

i. p1p2

ii. (1–p1) p2

iii. 1–(1–p1)(1–p2)

iv. p1+p2 = 2p1p2

Answer :

If the events are said to be independent, if the occurrence or non occurrence of one does not affect the probability of the occurrence or non occurrence of other.


i. p1p2


p1p2=P(A)P(B)


Both events A and B will occur


ii. (1–p1) p2


(1–p1) p2=[1–P(A)]P(B)



Event A does not occur but event B occur.


iii. 1–(1–p1)(1–p2)


1–(1–p1)(1–p2)=[1–(1–P(A))(1–P(B))]



At least one of the event will occur


iv. p1+p2 = 2p1p2


p1+p2 = 2p1p2


P(A)+P(B)=2P(A)P(B)


P(A)+P(B)–2P(A)P(B)=0


P(A)–P(A)P(B)+P(B)–P(A)P(B)=0


P(A)[1–P(B)]+P(B)[1–P(A)]=0




Exactly one of A and B occurs


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