Let A and B be tw

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