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week2_F10 - Online EE131A TA session Week 2 TA Ni-Chun Wang...

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Online EE131A Online EE131A TA session : Week 2 TA: Ni-Chun Wang [email protected]
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Review : Axioms of Probability (1) Sample space S . Events A, B S . ( ) • I. 0 P( A ) • II. P( S ) = 1 • III. If A B = , then P( A B ) = P( A ) + P( B ). • III’ If A 1 A 2 are mutually disjoint (i e A i A j III . If , , …, are mutually disjoint (i.e., = , for all i and j , i j), then ( ) i=1 i i=1 i . P P = A A 2
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Review : Axioms of Probability (2) Corollaries: ( C ) ( ) ( i C S ) • 1. P( A ) = 1 – P( A ). (since A A = • 2. P( A ) 1. • 3. P( ) = 0. (since S C = ) • 4 P( A B ) = P( A ) + P( B ) – P( A B ) 4. ) P( ) P( ) . P( A B C ) = P( A ) + P( B ) + P( C ) – P( A B ) – P( B C ) P( A C ) P( A B C ) ) – P( ) + P( ). • 5. If A B , then P( A ) P( B ). 3
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1. Let the events A and B have P(A) = x, P(B) = y and P(A B) Fi d P(A B) P(A B ) P(A B ) B) = z. Find P(A B), P(A c B c ), P(A c B c ), P(A B c ), P(A c B). – P(A B) = P(A) + P(B) – P(A B) => z = x + y – P(A B) => P(A B) = x + y – z. – P(A c B c ) = P((A B) c ) = 1 - P(A B) = 1 – z – P(A c B c ) = P((A B) c ) = 1 - P(A B) = 1 – (x + y – z) DeMorgan’s Rules P(A B c ) = P(A) – P(A B) = x – (x + y – z) = z – y P(A c B) = P(A c ) +P(B) – P(A c B) = P(A c ) +P(B) –(P(B) – P(A B)) = 1 – z + y P(A c B) = P((A B c ) c ) = 1 – P(A B c ) = 1 – z + y 4
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2. A box contains 10 white balls, 20 reds and 30 greens. Draw 5 without replacement. Find the
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