Section 2.4  2.5 Probability (p.55)
2.54 Suppose that in a senior college class of 500 students it is found that
210 smoke, 258 drink alcoholic beverage, 216 eat between meals, 122 smoke and
drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages,
97 smoke and eat between meals, and 52 engage in all three of these bad health
practices. If a member of this senior class is selected at random, find the prob
ability that the student
(a) smokes but does not drink alcoholic beverages;
sol)
Let
A
be the event that students smoke,
B
be the event that students drink
alcoholic beverage, and
C
be the event that students eat between meals.
P
(
A
∩
B
0
) =
P
(
A
)

P
(
A
∩
B
) =
210
500

122
500
=
88
500
(b) eats between meals and drinks alcoholic beverages but does not smoke;
sol)
P
(
C
∩
B
∩
A
0
) =
P
(
B
∩
C
)

P
(
A
∩
B
∩
C
) =
83
500

52
500
=
31
500
(c) neither smokes nor eats between meals.
sol)
P
((
A
∪
C
)
0
) = 1

P
(
A
∪
C
) = 1

329
500
=
171
500
2.56 From past experiences a stockbroker believes that under present economic
conditions a customer will invest in taxfree bonds with a probability of 0.6,
will invest in mutual funds with a probability of 0.3, and will invest in both
taxfree bonds and mutual funds with a probability of 0.15. At this time, find
the probability that a customer will invest
(a) in either taxfree bond or mutual funds;
sol)
Let
A
be an event that a customer will invest in taxfree bonds and
B
be an
event that a customer will invest in mutual funds.
Then,
P
(
A
) = 0
.
6,
P
(
B
) = 0
.
3, and
P
(
A
∩
B
) = 0
.
15.
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) = 0
.
6 + 0
.
3

0
.
15 = 0
.
75
(b) in neither taxfree bonds nor mutual funds.
sol)
P
((
A
∪
B
)
0
) = 1

P
(
A
∪
B
) = 1

0
.
75 = 0
.
25
1
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2.60 A pair of fair dice is tossed. Find the probability of getting
(a) a total of 8;
sol)
Let
A
be an event that getting a total of 8.
A
=
{
(2
,
6)
,
(3
,
5)
,
(4
,
4)
,
(5
,
3)
,
(6
,
2)
}
P
(
A
) =
5
36
(b) at most a total of 5.
sol)
Let
B
be an event that getting at most of a total of 5.
B
=
{
(1
,
1)
,
(1
,
2)
,
(2
,
1)
,
(1
,
3)
,
(2
,
2)
,
(3
,
1)
,
(1
,
4)
,
(2
,
3)
,
(3
,
2)
,
(4
,
1)
}
P
(
B
) =
10
36
=
5
18
2.62 If 3 books are picked at random from a shelf containing 5 novels, 3 books
of poems, and a dictionary, what is the probability that
(a) the dictionary is selected?
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 Fall '08
 Sally
 Conditional Probability, Probability, Alcoholic beverage

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