The probability that the plane will crash is
P(M and B1 and B2) = [P(M)][ P(B1)][ P(B2)]
6.69 P( wireless Web user uses it primarily for e-mail) = .69
6.70
6.71 P(A and B) = .36, P(B) = .36 + .07 = .43
P(A | B) =
837.
43.
36.
)B(P
)BandA(P ==
6.72 P(A and B) = .32, P(AC and B) = .14, P(B) = .46, P(BC) = .54
6.73
6.74 P(F | D) =
526.
038.
020.
)D(P
)DandF(P ==
6.75 Define events: A = crash with fatality, B = BAC is greater than .09)
6.76 P(CFA I | passed) =
327.
698.
228.
)passed(P
)passedandICFA(P ==
246.
346.
)B(P
6.78 P(A) = .40, P(B | A) = .85, P(B | AC ) = .29
P(B ) = .34 + .174 = .514
P(A | B) =
661.
514.
34.
)B(P
)BandA(P ==
6.80 Define events: A, B, C = airlines A, B, and C, D = on time
P(A) = .50, P(B) = .30, P(C) = .20, P(D | A) = .80, P(D | B) = .65, P(D | C) = .40
P(D) = .40 + .195 + .08 = .675
P(A | D) =
593.
675.
40.
)D(P
)DandA(P ==
6.81 Define events: A = win series, B = win first game
P(A) = .60, P(B | A) = .70, P(B | AC ) =.25
6.82
6.83
6.84 Sensitivity = P(PT | H) = .920
Specificity = P(NT |
C
H
) = .973
6.85
P(PT) = .0164 + .6233 = .6397
P(NT) = .0036 + .3567 = .3603
P(C | PT) =
0256.
6397.
0164.
)PT(P
)PTandC(P ==
6.87 Define events: A = win contract A and B = win contract B
a P(A and B) = .12
b P(A and BC) + P(AC and B ) = .18 + .14 = .32
c P(A and B) + P(A and BC ) + P(AC and B ) = .12 + .18 + .14 = .44
6.89 Define events: A = woman, B = drug is effective
749.
)B(P
6.91 P(Idle roughly)
= P(at least one spark plug malfunctions) = 1– P(all function) = 1 – (.90
4
) = 1-.6561 = .3439
6.92
P(no sale) = .65 + .175 = .825
6.93 a P(pass) = .86 + .03 = .89
b P(pass | miss 5 or more classes) =
250.
12.
03.
03.09.
03.
)classesmoreor5miss(P
)classesmoreor5missandpass(P ==
+
=
6.94 Define events: R = reoffend, D = detained
a P(D) = P(R and D) + P(R
C
and D) = .1107 + .2263 = .3370
P(R| D) =
3285.
3370.
1107.
)D(P
)DandR(P ==
C
6.95 a P(excellent) = .27 + .22 = .49
b P(excellent | man) =
44.
50.
22.
06.12.10.22.
22.
)man(P
)excellentandman(P ==
+++
=
6.96
6.97 Define events:
1
A
= Low-income earner,
2
A
= medium-income earner,
3
A
= high-income
earner, B = die of a heart attack, BC survive a heart attack
P(BC ) = .1848 + .4459 + .2790 = .9097
P(
| BC ) =
2031.
9097.
1848.
)B(P
)BandA(P
C
C
1==
6.98 Define the events:
= envelope containing two Maui brochures is selected,
2
A
= envelope
containing two Oahu brochures is selected,
3
A
= envelope containing one Maui and one Oahu
brochures is selected. B = a Maui brochure is removed from the selected envelope.
6.99 Define events: A = purchase extended warranty, B = regular price
a P(A | B) =
2692.
78.
21.
57.21.
21.
)B(P
)BandA(P ==
+
=
6.100 Define events: A = company fail, B = predict bankruptcy
6.101 Define events: A = job security is an important issue, B = pension benefits is an important
issue
6.102 Probabilities of outcomes: P(HH) = .25, P(HT) = .25, P(TH) = .25, P(TT) = .25
P(TT | HH is not possible) = .25/(.25 + .25 + .25) = .333
6.103 P(T) = .5
Case 6.1
Case 6.2
Probability Bases Probability Joint
Outcome of outcome Occupied Outs of scoring Probability
1 .75 2nd 1 .42 .3150
Case 6.3
0 outs:
Probability of scoring any runs from first base = .39
Probability of scoring from second base = probability of successful steal
probability of scoring
1 out:
Probability of scoring any runs from first base = .26
2 outs:
Probability of scoring any runs from first base = .13
Case 6.4
Age 25: P(D) = 1/1,300
P(D and PT) = (1/1,300)(.624) = .00048
P(D and NT) = (1/1,300)(.376) = .00029
P(
C
D
and PT) = (1,299/1,300)(.04) = .03997
Age 30: P(D) = 1/900
P(D and PT) = (1/900)(.710) = .00079
P(D and NT) = (1/900)(.290) = .00032
Age 35: P(D) = 1/350
P(D and PT) = (1/350)(.731) = .00209
P(D and NT) = (1/350)(.269) = .00077
Age 40: P(D) = 1/100
P(D and PT) = (1/100)(.971) = .00971
P(D and NT) = (1/100)(.029) = .00029
Age 45: P(D) = 1/25
P(D and PT) = (1/25)(.971) = .03884
Age 49: P(D) = 1/12
P(D and PT) = (1/12)(.971) = .08092
P(D and NT) = (1/12)(.029) = .00242
P(
C
D
and PT) = (11/12)(.343) = .31442
Case 6.5
The probability that 23 people have different birthdays is .4927. The probability that at least two
people have the same birthday is 1 − .4927 = .5073.