- #1

CoinToss

- 11

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## Homework Statement

Given P(AUBUCUD), expand

## The Attempt at a Solution

I approached the solution by procedurally drawing Vann Diagrams, building from AUB to AUBUCUD (Not included); Please do check if my line of reasoning is sound.

(let "n" be the intersection, AND)

1) P(AUB): P(A) + P(B) - P(AnB) [subtract the extra section, this is repeated at the end of subsequent steps]

2) P((AUB)UC): P(AUB) + P(C) - P((AUB)nC)

3) P((AUBUC)UD): P((AUB)UC) + P(D) - P((AUBUC)nD)

Substituting backwards, hence

A(AUBUCUD)= P(AUB) + P(C) - P((AUB)nC) + P(D) - P((AUBUC)nD)

A(AUBUCUD)= P(A) + P(B) - P(AnB) + P(C) - P((AUB)nC) + P(D) - P((AUBUC)nD) (Solved)

Also, do inform me if there is any more efficient way to put this. Thank you for your time.