A partition of the sample space n is a collection of

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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).

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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:

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