This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: STAT 400 HW3 Solution 2.3 Conditional Probability 1041 2.32 (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(AB) = m = 1 — 0. P(B) .6 “ 2.412 (a) v
{D NIH rx
n
v A
0"
v
ANA
0:
AA/\
non—I NIH NIHI
N) [OH—l MID4 A
9..
V
93.}0.
g ._
A
wit
v
M
/—\
ton—n
v
~41 N 2.5 Bayes’ Theorem 2.52 (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
2.56 (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
2.53 (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. ...
View
Full
Document
This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.
 Fall '05
 TBA

Click to edit the document details