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

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