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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