Events A and B are independent, events A and C are mutually exclusive, and events B and C are independent. If P(A) = 1/2; P(B) = 1/4; P(C) = 1/8; what is P(A∪B∪C)?

Question

Events

A

and

B

are independent, events

A

and

C

are mutually exclusive, and events

B

and

C

are independent.
If

P (A) = 12; P (B) = 14; P (C) = 18

; what is

P (A \cup B \cup C)

?

Answer 1

Note that the event

A \cup B \cup C

can happen in the following two disjoint ways: (i)

B

holds or (ii)

B

fails and one of

A

or

C

holds.
The probability of (i) is

1 / 4

.
For probability of (ii) we need to work somewhat harder. Since

A

and

C

are mutually exclusive, we want

Pr (B^{'} \cap A) + Pr (B^{'} \cap C)

. Here

B^{'}

denotes the complement of

B

. The required probabilities can be found by independence.
It remains to put the pieces together.

Answers (1)