Q. 2.13 A certain town with a population... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 2: Q. 2.13 (page 49)

A certain town with a population $100, 000$ has $3$ newspapers: $I, I I,$ and $I I I .$ The proportions of townspeople who read these papers are as follows:
$I : 10$ percent $I$ and $I I : 8$ percent $I$ , $I I$ and $I I I : 1$ percent
$I I : 30$ percent $I$ and $I I I : 2$ percent
$I I I : 5$ percent $I I$ and $I I I : 4$ percent
(The list tells us, for instance, that $8000$ people read newspapers $I$ and $I I$ )
$(a)$ Find the number of people who read only one newspaper.
$(b)$ How many people read at least two newspapers?
$(c)$ If $I$ and $I I I$ are morning papers and $I I$ is an evening paper, how many people read at least one-morning paper plus an evening paper?
$(d)$ How many people do not read any newspapers?
$(e)$ How many people read the only one-morning paper and one evening paper?

Short Answer

Expert verified

$(a) 20, 000 (b) 12, 000 (c) 11, 000 (d) 68, 000 (e) 10, 000$

Step by step solution

Given Information.

A certain town with a population $100, 000$ has $3$ newspapers: $I, I I,$ and $I I I$ . The proportions of townspeople who read these papers are as follows:

$I : 10$ percent $I$ andlocalid="1648886719226" $I I : 8$ percent $I$ , $I I$ and $I I I : 1$ percent

$I I : 30$ percent $I$ and $I I I : 2$ percent

$I I I : 5$ percent $I I$ and $I I I : 4$ percent

Part (a) Explanation.

$I$ only $+ I I$ only $+ I I I$ onlylocalid="1648886840081" $1000 + 19000 + 0 = 20000$ .

Part (b) Explanation.

$(I$ and $I I$ only localid="1648886856146" $) + (I I$ and localid="1648886864731" $I I I$ only $) + (I$ and $I I I$ only $) + (I$ , $I I$ andlocalid="1648886873356" $I I I)$ $= 7, 000 + 3, 000 + 1, 000 + 1, 000 = 12, 000$ .

Part (c) Explanation.

$(I$ and $I I$ only $) + (I I I$ andlocalid="1648886895972" $I I$ only) $+ (I, II$ and $I I$ only $) = 7, 000 + 3, 000 + 1, 000 = 11, 000$ .

Part (d) Explanat\ion.

From Part (a) we have $68000$ .

Part (e) Explanation.

$(I$ and $I I$ only $) + (I I I$ and $I I$ only $)$ $= 7, 000 + 3, 000 = 10, 000$ .

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Short Answer

Step by step solution

Given Information.

Part (a) Explanation.

Part (b) Explanation.

Part (c) Explanation.

Part (d) Explanat\ion.

Part (e) Explanation.

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