Q1 Express the following probability in terms of A B Cs and

Q1:

Express the following probability in terms of A, B, C\'s and intersections. Your expression may include: 1, P(A), P(B), P(C), P(AnB), P(AnC), P(BnC) and P(AnBnc) only P ((AUB)nc\')

Solution

q1:

P([(A U B) n C]\')

= 1 - P[(A U B) n C]

= 1 - {P[(A U B)] + P(C) - P[(A U B) U C]}

= 1 - P[(A U B)] - P(C) + P[(A U B) U C]

= 1 - P[(A U B)] - P(C) + [P(A) + P(B) + P(C) - P(A n B) - P(B n C) - P(A n C) + P(A n B n C)]

= 1 - P(A U B) - P(C) + P(A) + P(B) + P(C) - P(A n B) - P(B n C) - P(A n C) + P(A n B n C)

= 1 - [P(A) + P(B) - P(A n B)] - P(C) + P(A) + P(B) + P(C) - P(A n B) - P(B n C) - P(A n C) + P(A n B n C)

= 1 - P(A) - P(B) + P(A n B) - P(C) + P(A) + P(B) + P(C) - P(A n B) - P(B n C) - P(A n C) + P(A n B n C)

= 1 - P(B n C) - P(A n C) + P(A n B n C) [ANSWER]

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