Chapter 2. Probability
2.1 a. There are 330 blues songs out of 27,333. 330/27,333 = 0.0121 b. With 330 blues, 537 jazz,
()
PA
2.3
( ) ( ) ( ) ( ) ( )P A B C P A P B P C P A B
( ) ( ) ( ),P A C P B C P A B C
2.4
( ) ( ) ( ) ( ) ( )P A B C P A P B P C P A B
( ) ( ) ( ),P A C P B C P A B C
so, 0.89 =
2.5 a. The woman has 30 pairs of shoes. 13/30 = 0.4333 = 43.33% will make her taller.
2.6 Because eight children do not like either, 22
2.7 a. Answers will vary. b. Answers will vary. One possibility is
{ | 0}.S x x
c. Answers
2.8 Because each flip has a 0.5 probability of being either a head or a tail,
P
(HHHHT) =
5
(0.5)
2.9 a. There were a total of 12 pizzas. Five had bacon (the two bacon and 3 meat lovers), so 5/12
2.14 Note in the Venn diagram that the 35% who like
P
2.15 a.
{1,3,4,5,6}.ABC
( ) 4 / 6 2 / 3.P A B C
Using Theorem 2.23, we would
2.16 DeMorgan’s first law says
( ) .
cc
ii
AA
This
2.17
P
(P) = 1/3.
P
({G, P), (Y, P)}) =
1/ 3 1/ 2 1/ 3 1/ 2
= 1/3.
(( , ),( , , ))P G P G Y P
2.18 With three dice, there are
5
66666 6
= 7776 possible combinations. Six of these
2.19 There are 2 possibilities for the first number, 10 for the second, and 46 for the third.
2.20 89 = M + S + A – (M and S) – (M and A) – (S and A) + (M and S and A).
2.21 a. Because each person could be either male or female,
7
2
= 128. b.
7
2
= 21. c.
0
| | 1,A
7
| | 1,A
7
2.22
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ),P A B C P A P B P C P A B P A C P B C P A B C
2.23
2.24 Proof:
( ) ( ( )) ( ) ( ( ) ( ) ( )) ( ( ))P A B C P A B C P A P B P C P B C P A B C
2.25 Proof:
( ) (( ) )) ( ) ( ) (( ) )P A B C D P A B C D P A B C P D P A B C D
P
P
2.27 a. Yes.
( ) ( ) ( ) ( )P A B P A P B P A B
, and
( ) 0.P A B
b. Yes.
2.28 Because each pen works 25% of the time (i.e.,
P
(pen works) = 0.25 for all pens),
P
(one
2.29 For the sum of the first two to equal the third, you must have (1,1,2), (1, 2,3), (2,1,3),
2.30 a. (9/20)(8/19) = 0.1895 b. This is the complement of both chocolate chip, so 1 –
2.31 a. Fix Alice at position 1 (because rotations do not
count). There are four people who can sit in position 2. For
2.32 There are 22 total socks in the drawer.
P
(matching pair) =
P
(both white) +
P
(both black)
P
2.33
1
( ) 1/ 216PB
because this must be (1,1,1).
2
( ) 8/ 216PB
because this must be (1,1,1),
2.35 Let
g
A
be the event that person g draws his/her number. The probability there is no winner