[craigt]

A manager at a convenience store and gas station tabulates the following facts
45% of all customers purchase gas
31% of all customers purchase cigarettes
60% of all customers buy either gas or a slurpee
16% of all customers buy both gas and cigarettes
13% of all customers buy both gas and a slurpee
8% of all customers buy both cigarettes and a slurpee
5% of all customers buy all three

A) what is the probability that a customer buys either gasoline or cigarettes
B)what is the probability that a customer buys a slurpee?
C)Is the purchase of any of the three items independent of the purchase of any others?
Explain.

I have tried absolutely everything I can think of to try and answer this question, I have tried going through my notes, I have read and re-read the section of my text book but can not figure this problem out.
I tried to create a Venn diagram to simplify the problem but came up with having one piece of data left over which was the 60% I could not figure out where to put it.
For the first question I originally figured it would be as easy as entering the data of 45% + 31% = 76%
But then realized that there was more data then that to put in to figure out the solution.

I am seriously at my end with this question I have been trying to figure out for 5 days now.
I am not looking for the answer but if someone can give me some sort of advice as to how to get started that would be very much appreciated

[mama na bojana]

Hi,

The problem look like complicated one but it is simple
The idea with Vene diagram is correct and perfect way
Using:

* for union
+ for intersection
/ for subtract


A.
5=No(C+G+S)
8=No(G+S) mean (G+S)/(C+G+S)=3 gas and slurpee but no cigarettes
Following the same way
We have people buying only gas or only cigarettes, and these buying gas and cigarettes

45=No(G)
31=No(C)
16=No(G+C) mean
45-16 only gas G/C
31-16 only cigarettes C/G
16 both,
These three sets are without any common element so called DISJUNCTIVE SETs?(I am sorry but I am from different country of origin I am trying to find the proper expressions, and maybe I am wrong? about the name only, the explanation is correct)

and in total [45-16]+[31-16]+16= all possibilities are included, take care we are not talking at all about the people whom are buying slurpee, this is irrelevant, and here you can work with a simplified model of two sets.

Try to solve the rest
Regards