SOLUTION: 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 Busines

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Question 150592This question is from textbook a survey of mathematics with applications
: 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
b) on vacation given the traveler was male
c) female given the traveler was on business
(Give solutions as fractions in lowest terms.)
can someone please help me?
This question is from textbook a survey of mathematics with applications

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |    72  |   74    |  146
-------------------------------------
Total      |   129  |  166    |  295

You see that there are 129 Males out of 295 Travelers.
So you put 129 ove 295 and get the fraction 129%2F295
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%2F129 and reduce
that reduces to 24%2F43

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

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%2F129 which
doesn't reduce.

Edwin