Solution Found!
Let S = A1 ? A2 ? · · · ? Am, where events A1,A2, . . .
Chapter 1, Problem 15E(choose chapter or problem)
PROBLEM 15E
Let S = A1 ∪ A2 ∪ · · · ∪ Am, where events A1,A2, . . . ,Am are mutually exclusive and exhaustive.
(a) If P(A1) = P(A2) = · · · = P(Am), show that P(Ai) = 1/m, i = 1, 2, . . . ,m.
(b) If A = A1 ∪A2∪· · ·∪Ah, where h < m, and (a) holds, prove that P(A) = h/m.
Questions & Answers
QUESTION:
PROBLEM 15E
Let S = A1 ∪ A2 ∪ · · · ∪ Am, where events A1,A2, . . . ,Am are mutually exclusive and exhaustive.
(a) If P(A1) = P(A2) = · · · = P(Am), show that P(Ai) = 1/m, i = 1, 2, . . . ,m.
(b) If A = A1 ∪A2∪· · ·∪Ah, where h < m, and (a) holds, prove that P(A) = h/m.
ANSWER:
Answer:
Step1 of 3:
Let Since
,
….
are mutually exclusive.
Therefore, ,
And since exhaustive also
Step2 of 3:
a). If P() = P(
) = ….= P(
) . To show that P(