Bill's hamburger palace has several stores in the area of Gary, Indiana.
When interviewing applicants for server positions, the owner would
like to include information on the amount of tip a server can expect
to earn per check (or bill). A study of 500 recent cheks indicated the
server earned the following tip.

Amount of tip               Number
$0 to $5                      200
$5 to $10                     100
$10 up to $20                  75
$20 to $50                     75
$50 or more                    50

Total                          500

What is the probability of a tip of $50 or more?
Are the categories $0 to $5 up to $10 and so on considered mutually exclusive
If the probabilities associated with each outcome were totaled, what
would that total be?
What is the probability of a tip of up to $10?
What is the probably of a tip of less than $50?

Thanks!

Dear rhemaword,


The probability of getting a tip of $50 or more is

  50/500  =  .1
  
          =  10%.
          

The categories currently defined are mutually exclusive, since a server
can only belong to one or the other. But a new category "$0 to $10" would
not be mutually exclusive with the category "$0 to $5", for instance,
because a server could simultaneously belong to both.


If we total the probabilities of a complete set of mutually exclusive
outcomes, the result must be 100%.


The probability of getting a tip up to $10 is

  (200+100)/500  =  300/500
  
                 =  .6
                 
                 =  60%.
                 

We know from an earlier calculation that the probability of getting a tip
of $50 or more is 10%, so the probability of getting a tip under $50 is

  100% - 10%  =  90%.
  
  
Regards,

leapinglizard

Thanks so very much for your help!!

I could be wrong, but isn't it pretty much the following:

1.  (50/500)=.10 or %10
2.  Note sure, but I want to say yes
3.  (200/500)+(100/500)+(100/500)+(75/500)+(75/500)+(50/100)=1
4.  (300/500) = .60 or %60
5.  (450/500) = .90 or %90

But of course this is just my free comment.

This is really what three should be

3.  (200/500)+(100/500)++(75/500)+(75/500)+(50/100)=1