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. p1p2ii. (1–p1) p2iii. 1–(1–p1)(1–p2)iv. p1+p2 = 2p1p2

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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