Let A and B be two independent events such that P(A) = p 1 and P(B) = p 2 . Describe in words the events whose probabilities are: i. p 1 p 2 ii. (1–p 1 ) p 2 iii. 1–(1–p1)(1–p2) iv. p 1 +p 2 = 2p 1 p 2

Question

Philoid · Accepted 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

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

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