Question 150592
<pre><font size = 4 color = "indigo"><b>
I'm really having diffuculties trying to understand
this question.

11. (3 pts) The results of a survey for an airline 
are shown below:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |    72  |   74    |  146
-------------------------------------
Total      |   129  |  166    |  295
Use the chart to find the probability that the traveler was 
a)	male 

Well, let's see how many of the Total 295 were males.
I'll color the Male column red:

Traveler   |   <font color = "red">Male</font> |  Female | Total
-------------------------------------
Business   |    <font color = "red">57</font>  |   92    |  149
Vacation   |    <font color = "red">72</font>  |   74    |  146
-------------------------------------
Total      |   <font color = "red">129</font>  |  166    |  295

You see that there are 129 Males out of 295 Travelers.
So you put 129 ove 295 and get the fraction {{{129/295}}}
and that's the answer.


b)	on vacation given the traveler was male

Since we are given that the traveler was male, then we 
can eliminate everything but just what is given, the
Male column. So all that remains in the chart is this:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |         |     
Vacation   |    72  |         |  
-------------------------------------
Total      |   129  |         |  

So there are 72 males on on vacation out of 129 given males.
So we put 72 over 129 and get {{{72/129}}} and reduce
that reduces to {{{24/43}}}

-------------------------

c)	female given the traveler was on business 
       (Give solutions as  fractions in lowest terms.)


Since we are given that the traveler was on business, we
can eliminate everything but just what is given, the
Business row. So all that remains in the chart is this:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |        |         |  
-------------------------------------
Total      |        |         |  

So there are 92 females on business out of 149 given travelers on
business. So we put 92 over 129 and get {{{92/129}}} which
doesn't reduce.

Edwin</pre>