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Example Class 1 (sln)

Example Class 1 (sln) - ² ∪ ³ = ² ³ − ² ∩ ³ =...

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The University of Hong Kong Department of Statistics and Actuarial Sciences STAT1801 Example Class 1 Solution Example 1 (a) 8! = 40320 (b) (7!)(2!) = 10080 (arrange (A,B), C, D, E, F, G, H in a row) (c) (4!)(4!)(2) = 1152 (MWMWMWMW or WMWMWMWM) (d) (4!)(5!)= 2880 (arrange (A,B,C,D,E), F, G, H in a row) (e) (4!)(2 4 ) = 384 (arrange (A,B), (C,D), (E,F), (G,H) in a row) Example 2 (a) Total combinations = 52 5 ± = 2 598 960 Favourable outcomes = 40 Therefore, P(Straight flush) = 40/2598960 = 0.00154% (b) Favourable outcomes = 4 3 ± 4 2 ± (13)(12) = 3744 P(Full house) = 3744/2598960 = 0.144% (c) Favourable outcomes = [4 5 (10) 40] = 10200 P(Straight) = 0.392% (d) Favourable outcomes = [(13) 4 3 ± 48 2 ± − 3744] = 54912 P(Three of a kind) = 2.11% Example 3 A = metropolitan newspaper, B = local afternoon paper Then, P(A) = 0.6, P(B) = 0.8, ? ( ² ∩ ³ ) = 0.5 (a) P(At least one of the two newspapers) =

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Unformatted text preview: ? ( ² ∪ ³ ) = ? ( ² ) + ? ( ³ ) − ? ( ² ∩ ³ ) = 0.9 (b) P(Exactly one of the two newspapers) = P(A only) + P(B only) = ? ( ² \( ² ∩ ³ )) + ? ( ³ \( ² ∩ ³ )) = ? ( ² ) − ? ( ² ∩ ³ ) + ? ( ³ ) − ? ( ² ∩ ³ ) = 0.4 Example 4 A = teeth cleaned, B = cavity filled, C = tooth extracted P(at least one of these things done) = 0.47+0.29+0.09-0.03-0.13-0.02+0.01 = 0.68 Example 5 (a) A’ = {(1,1), (2,1), (2,2), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (4,4), (5,1), (5,2), (5,3), (5,4), (5,5), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}  a total of 21 possible outcomes ? ( ± ′ ) = 21 36 = 7 12 (b) ± ∩ ² = { (2,6), (3,6), (4,6), (5,6), (3,5), (4,5) } ? ( ± ∩ ² ) = 6 36 = 1 6 (c) A\B = { (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (3,4) } ? ( ± \ ² ) = 9 36 = 1 4...
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Example Class 1 (sln) - ² ∪ ³ = ² ³ − ² ∩ ³ =...

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