stat400sln3 - STAT 400 HW3 Solution 2.3 Conditional...

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Unformatted text preview: STAT 400 HW3 Solution 2.3 Conditional Probability 1041 2.3-2 (3.) TR, 392 6E1 649 (0) “8—23- (d) The proportion of women who favor a gun law is greater than the proportion of men who favor a gun law. 2.36 Let A = {3 or 4 kings}, B = {2, 3, or 4 kings}. P(A n B) _ N(A) P(B) ‘ M‘B‘) P (AIB) 2.4.2 (3.) P(A n B) P(A)P(B) = (0.3)(0.6) = 0.18; P(A u B) : P(A) + P(B) — P(A n B) = 0.3 + 0.6 — 0.18 = 0.72. (b) P(A|B) = m = 1 — 0. P(B) .6 “ 2.4-12 (a) v {D NIH r-x n v A 0" v ANA 0: AA/\ non—I NIH NIH-I N) [OH—l MID-4 A 9.. V 93.}0. g ._ A wit- v M /—\ ton—n v ~41 N 2.5 Bayes’ Theorem 2.5-2 (3.) P(G) = P(A n G) + P(B n G) = P(A)P(G IA) + P(B)P(G | B) = (0.40)(0.85) + (0.60)(0.75) = 0.79; _ P(AnG') (D.40)(0.85) _ 0.79 “0‘43" ‘1 i J 3 5 1 15 3 2.5-6 (3) P(R)—Z'2—5+Z'§§—fi, (b>P(Y)=1—P(R>=T76; 1 15 1‘23 *1 ‘0 9.3 1.13 ‘ 4 25 4 25 2.5-3 (a) P(AD) = (0.02)(0.92)+(0.98)(0.05) :0.0674;[.1in] ' (0.9s)(0.05) _ 0.0490 _ . (b) “NI/w) ' 0.0674 ‘ 0.0674 " 0‘7270’ _ (0.02)(0.92) _ 0.0184 _ . “MAM ’ 0.0674 ’ 0.0674 “ 0'2730’ (c) P(ND) = (0.02)(0.08) + (0.98)(0.95) = 0.9320; (0.98)(0.95) _ 0.9310 _ . PW IND) 0.9326 " 0.9326 ‘ 0'9983’ fi (0.02)(0.08) _ 0.0016 _ I HA'ND) * 0.9326 — 0.9326 — 0‘0017’ (d) Yes, it is terrible for a doctor to say a child is abused when in fact he or she is not abused; yet the conditional (posterior) probability of that is 0.7270. ...
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stat400sln3 - STAT 400 HW3 Solution 2.3 Conditional...

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