2.4
(a)
(b)
(c)
2.6
(a) Los Angeles, Long Beach, Pasadena, Anaheim, Santa Maria, Westwood
(b) San Diego, Long Beach, Pasadena, Anaheim, Santa Maria, Westwood
(c) Santa Barbara
(d) Empty set
(e) San Diego, Long Beach, Santa Barbara
(f) San Diego, Santa Barbara, Long Beach
(g) Los Angeles, Santa Barbara, Anaheim
(h) Los Angeles, Pasadena, Santa Maria, Westwood
(i) Los Angeles, Pasadena, santa Maria, Westwood
2.10
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(a) E
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(b) F
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(c) G
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(d) E
U F|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(e) E intersection F
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(f) F
U G|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(g) E
U F'|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(h) E intersection G'
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
(i) F' intersection E'
|
0 |
1 |
2 |
3 |
4 |
|
|
0 |
(0,0) |
(0,1) |
(0,2) |
(0,3) |
(0,4) |
|
1 |
(1,0) |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
|
2 |
(2,0) |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
|
3 |
(3,0) |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
|
4 |
(4,0) |
(4,1) |
(4,2) |
(4,3) |
(4,4) |
|
5 |
(5,0) |
(5,1) |
(5,2) |
(5,3) |
(5,4) |
2.12
(a)
S={(0,0,0), (0,0,1), (0,1,0), (1,0,0), (1,1,0), (1,0,1), (0,1,1), (1,1,1)}
A
={(1,0,1), (0,1,1), (1,1,1)}B={(0,1,1)}
C={(1,0,1)}
(b) A and B and A and C are not mutually exclusive, B and C are mutually exclusive
2.20
200-(138+115)+91=38
2.22
(a) 12
(b) 6
(c) 20
2.25
2.27
Facts that you need to use
1. 
2. Probability of any event is between 0 and 1. Therefore
(a)
(b)
2.31
2.33
2.34
(a) Postulate 1
(a) Postulate 2
2.36
(a)
(b)
(c)
(d)
(e)
(f)
2.39
(a) .12+.17=.29
(b) .17+.34+.29=.80
(c) .34+.17+.12=.63
(d) .34+.29+.08=.71
2.42
Let P(A)=4p, P(B)=2p, P(C)=2p, P(D)=p. Then 9p=1.
p=1/9.
(a) 2/9
(b) 1-4/9=5/9
2.47
(a) P(AUB) is less than P(A)
(b) P(A and B) exceeds P(A)
(c) P(AUB)=.72+.84-.52=1.04 exceeds 1.
2.53
.70+.64+.58+.58-.45-.42-.41-.35-.39-.32+.23+.26+.21+.20-.12=.94
2.55
(a) (6/10)/(4/10)=6/4 3 to 2
(b) (11/16)/(5/16)=11/5 11 to 5
(c) (7/9)/(2/9)=7/2 7 to 2 against it or 2 to 7
2.56
(a) 5/12+1/12=6/12=1/12; consistent
(b) 1/3+1/5=8/15 since this is not equal to 7/12; not consistent
2.64
2.69
2.75
(a) (18+36)/90=54/90=3/5
(b) (36+27)/90=63/90=7/10
(c) 18/90=2/10=1/5
(d) 27/90=3/10
(e) 18/(18+36)=18/54=1/3
(f) 27/(27+36)=27/63=3/7
2.76
(a) 1/3=(1/5)/(3/5)
(b) 3/7=(3/10)/(7/10)
2.83
Let A="patient survives"
B="body accepts the transpalant"
2.88
(a) (3/4)(1/4)(1/4)
(b) 3(3/4)(3/4)(1/4)=27/64
2.91
Let A="at least one of them has the deficiency"
A'="none of them has the deficiency"
P(A)=1-P(A')=1-(0.9)12=1-0.2824=0.7176
2.98
P(S)=0.6(.45)+0.15(0.70)+0.25(0.40)
2.104
P(A|E)=0.05/0.3425=0.1460
P(B|E)=0.08/0.3425=0.2336
P(C|E)=0.10/0.3425=0.2920
P(S|E)=0.1125/0.3425=0.3285
(a) Most likely cause is sabotage
(b) least likely cause is static electricity