Solution Found!
A partition of the sample space n is a collection of
Chapter , Problem 9(choose chapter or problem)
A partition of the sample space n is a collection of disjoint events 81 , ... , 8n such that n = U18i . (a) Show that for any event A, we have n P(A) = L P(A n 8i). i=l (b) Use part (a) to show that for any events A, B, and C, we have P(A) = P(A n B) + P(A n C) + P(A n BC n CC) - P(A n B n C).
Questions & Answers
QUESTION:
A partition of the sample space n is a collection of disjoint events 81 , ... , 8n such that n = U18i . (a) Show that for any event A, we have n P(A) = L P(A n 8i). i=l (b) Use part (a) to show that for any events A, B, and C, we have P(A) = P(A n B) + P(A n C) + P(A n BC n CC) - P(A n B n C).
ANSWER:a.
Step 1 of 6
Consider the partition of sample space as disjoint collection events as shown in the vein diagram below: