Probability question

I've been stuck on a portion of a stats question and was hoping someone could possibly help!

The manager of a gas station and convenience store tabulates the following facts:
60% of customers purchase gasoline (G)
38% of customers purchase cigarettes (C)
74% of customers purchase gasoline or a drink
18% of customers purchase gasoline and cigarettes
21% of customers purchase gasoline and a drink
15% of customers purchase cigarettes and a drink
3% of customers purchase all three items

What is the probability that a randomly selected customer purchases exactly one of the three items?

Thanks!

lea.g said:

I've been stuck on a portion of a stats question and was hoping someone could possibly help!

The manager of a gas station and convenience store tabulates the following facts:
60% of customers purchase gasoline (G)
38% of customers purchase cigarettes (C)
74% of customers purchase gasoline or a drink
18% of customers purchase gasoline and cigarettes
21% of customers purchase gasoline and a drink
15% of customers purchase cigarettes and a drink
3% of customers purchase all three items

What is the probability that a randomly selected customer purchases exactly one of the three items?

Thanks!

Click to expand...

Use a Venn diagram to see the problem graphically - it helps me.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Subhotosh Khan said:

Use a Venn diagram to see the problem graphically - it helps me.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Click to expand...

There are a few other parts to the question that I've been able to calculate:

The probability that a randomly selected customer purchases gasoline or cigarettes = .8
If we randomly select a customer, the probability that they purchase a drink = .35
The probability that a randomly selected customer purchases cigarettes, but not a drink = .23
Gasoline and drink are independant.

I drew a Venn diagram for this question (the probability that a randomly selected customer purchases exactly one of the three items), and my initial thought was to work backwards - start with a sample space of 1 and subtract the probabilities that occur together.

i.e. = 1 - .03 - .18 - .21 - .15 = .43

I realize this is wrong, and I can't seem to see what I'm missing here, so any help would be appreciated! I think I might be confusing myself even more by my venn diagram.

lea.g said:

I've been stuck on a portion of a stats question and was hoping someone could possibly help!

The manager of a gas station and convenience store tabulates the following facts:
60% of customers purchase gasoline (G)
38% of customers purchase cigarettes (C)
74% of customers purchase gasoline or a drink
18% of customers purchase gasoline and cigarettes
21% of customers purchase gasoline and a drink
15% of customers purchase cigarettes and a drink
3% of customers purchase all three items

What is the probability that a randomly selected customer purchases exactly one of the three items?

Thanks!

Click to expand...

Just to be definitive (and pedantic), I think this has to be rewritten/interpreted as
60% of customers purchase gasoline (G) and maybe other items
38% of customers purchase cigarettes (C) and maybe other items
74% of customers purchase gasoline or a drink (D) but not cigarettes
18% of customers purchase gasoline and cigarettes but not a drink
21% of customers purchase gasoline and a drink but not cigarettes
15% of customers purchase cigarettes and a drink but not gasoline
3% of customers purchase all three items

Thus, of those who bought cigarettes (38%), 18% bought gasoline and 15% bought a drink and so 5% bought only cigarettes. and to continue

Ishuda said:

Just to be definitive (and pedantic), I think this has to be rewritten/interpreted as
60% of customers purchase gasoline (G) and maybe other items
38% of customers purchase cigarettes (C) and maybe other items
74% of customers purchase gasoline or a drink (D) but not cigarettes
18% of customers purchase gasoline and cigarettes but not a drink
21% of customers purchase gasoline and a drink but not cigarettes
15% of customers purchase cigarettes and a drink but not gasoline
3% of customers purchase all three items

Thus, of those who bought cigarettes (38%), 18% bought gasoline and 15% bought a drink and so 5% bought only cigarettes. and to continue

Click to expand...

Perhaps I'm still not seeing it, because when I tried this approach for drinks, I get:

35% buy drinks, of those who buy drinks, 21% bought gasoline and 15% bought cigarettes, so -1% bought only drinks? Sorry if I'm still missing the point. I think I've been staring at this so long, that nothing seems to make sense!

lea.g said:

Perhaps I'm still not seeing it, because when I tried this approach for drinks, I get:

35% buy drinks, of those who buy drinks, 21% bought gasoline and 15% bought cigarettes, so -1% bought only drinks? Sorry if I'm still missing the point. I think I've been staring at this so long, that nothing seems to make sense!

Click to expand...

And you are getting 35% buy drinks from where?

EDIT: But I'm no longer sure that is the right interpretation. So what is the interpretation

Ishuda said:

And you are getting 35% buy drinks from where?

Click to expand...

It was one of the previous calculations. "If we randomly select a customer, what is the probability that she purchases a drink?"

I calculated that using the equation P(G or D) = P(G) + P(D) - P (G and D)
.74= .6 + P(D) - .21
P(D) = .35

That portion was marked as correct, so the answer should be right at .35