Transcript HW problems 3-2

HW problems 3-2
p. 121 #14. A study of 150 randomly selected American Airlines flights
showed that 108 arrived on time (DOT).
a) What is the probability of arriving late on an AA flight?
b) Is it unusual to arrive late on AA?
A: a) P(late on AA) = 42 / 150 = 0.28
b) Arriving late on AA is not unusual!
p. 122 # 17. a) Probability of randomly selecting person with b-day on
October 18.
b) Probability of birthday in October.
c) Probability of randomly selecting a person born on a day of the week
ending on y.
a)
b)
c)
P(Oct 18) = 1/ 365
P(October) = 31/365
P(‘birth on day ending in ‘y’) = 1
HW problems 3-3 and 3-4
Blood group and Rh types
4 Rh +
1 Rh -
Group B
. 130 # 13-20
a)
P(not gpA)
=60/100
b)
P(type Rh-)
=14/100
c)
P(gp A or ty Rh-) =(40+14–5)/100=0.39
d)
P(gp A or gp B) =50/100 disjoint
e)
P(not ty Rh+)
=14/100 see (b)
Group A
f)
P(gpB or ty Rh+) =0.1+0.86–0.08=0.88
Type
g)
P(gp AB or Rh+)
Rh factor
O
+
39
h)
P(A or O pr Rh+) =0.85+0.866
Totals
45
(0.39+0.35)
= .85+.86-.74
=0.97 (3 not Rh+ or AO)
Group AB
8 Rh +
2 Rh -
39 Rh +
6 Rh -
Group O
35 Rh +
5 Rh -
A
35
5
40
B
8
2
10
AB
4
1
5
Totals
86
14
100
p. 138 #11. a) What is the probability that 2 randomly selected people have b-day
on Nov. 27?
b) What is the probability that 2 randomly selected people have same b-day?
A: a) P(b-day of John and Jack on Nov 27) = 1/365 * 1/365 = 1/133225 =
0.00000751
b) P(same birthday) = 365 different DAYS* 1/365*1/365 = 1/ 365
HW problems 3-4 and 3-5
p. 139 #13. Acceptance sampling. If all items in sample without
replacement are good, batch accepted. Batch 5000 CDs, 3%
defective. Sample 12 at random.
a) What is the probability that the batch will be accepted?
A: a) P(batch accepted) = 0.97 12 = 0.694
p. 147 # 19-21 Titanic example.
Titanic Mortality Rate
Men
Survived
Died
P(man|died) = P(man & died)/P(died)
P(died |man) = P(man & died )/P(man)
P(A |B )=P( A and B) / P(B)
Women
Boys
Girls
332
318
29
27
1360
104
35
18
“At least one” event
• At least one = one or more
• Complement: none!
P(at least one girl among 3 children)
= 1- P(no girl)
boy-boy-boy
=1-1/8
boy-boy-girl
boy-girl-boy
=7/8
boy-girl-girl
=0.875
girl-boy-boy
girl-boy-girl
girl-girl-boy
girl-girl-girl
P(at least one poll within confidence
interval)
=1- P(no poll good)
=1- [ 0.05 5] = 0.9999997
Conditional probability
The conditional probability of the event
A given B is denoted by P(A | B) and
it is the probability that A occurs
knowing that B has occurred already
Subject
pregnant
Test positive
Negative
80
not pregnant
Total
Total
3
positive
83
5
11
14 not pregnant
negative
16
• 1 subject is selected randomly, find the
probability of a subject being positive, given
that she is pregnant.
P(pos|pregnant) = 80/85=0.941 or
= P(positive and pregnant)
P(pregnant)
happens always!
85 pregnant
= 80/99 = 0.964
85/99
Conditional Probability
Titanic
• P(man |died)
• P(died |men)
• P(boy or girl |survived)
• P(man or woman | died)
Titanic Mortality Rate
Men
Survived
Died
Women
Boys
Girls
332
318
29
27
1360
104
35
18
Titanic Mortality Rate
Men
Survived
Died
=m/w/b/g
Women
Boys
Girls
29
Total D/A
332
318
27
1360
104
35
18
1692
422
64
45
706
1517
2223
P(man|died) = P(man & died)/P(died) = 1360/1517=0.897
P(died |man) = P(man & died )/P(man) = 1360/1692=0.804
P(boy or girl |survived)=P( {boy or girl} & survived)/P(survived)=57/706=0.079
P(man or woman | died) )=P({man or woman}& died)/P(died)=1464/1517=0.965
NOTE:
P(man & died)
P(died)
=
1360 / 2223 = 1360 = 0.897
1517 / 2223
1517
HW problems 3-6
p. 155 #9. Probability of winning Mass Lotto:
6 numbers from 1,…,49
A: a) P(win) = 1/49C6= 1 / 13,983,816
p. 156 # 22 Board of directors. 12 members on board.
a) Elect chair, vice-chair, 2nd vice-chair, and secretary. How many
different slates?
b) Ethics subcommittee. 4 members. How many subcommittees
possible?
a)
b)
C,VC1,VC2, S: ORDER MATTERS! 12P4= 11,880
Subcommittee: ORDER DOES NOT MATTER!
12C4= 495