The manager of a gas station and convenience store tabulates the following facts:
40% of customers purchase gasoline (G).
36% of customers purchase cigarettes (C).
61% of customers purchase gasoline or a drink (D).
9% of customers purchase gasoline and cigarettes.
14% of customers purchase a gasoline and a drink.
15% of customers purchase cigarettes and a drink.
2% of customers purchase all three items.
(a) If we randomly select a customer, what is the probability that she purchases gasoline or cigarettes?
(b) If we randomly select a customer, what is the probability that

- anonymous

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- hartnn

P(A or B) = P(A)+ P(B)-P(A and B)
here, A = gasoline, B =cigarette

- hartnn

you know all 3, P(A),P(B),P(A and B)
just plug in values!

- anonymous

0.04+0.36-?

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## More answers

- hartnn

40% = 0.4
and P(G and C) is given as % = 0.09

- hartnn

9%

- anonymous

what about P(A and B)

- anonymous

oh I got it

- hartnn

what you got as final answer ?

- anonymous

what about b ?

- hartnn

complete question ?

- anonymous

i got 0.67

- anonymous

is that right?

- hartnn

lets check,
P(G or C) = 0.4+0.36-0.09 = 0.76-0.09 = 0.67
yes, you are correct :)

- anonymous

what about b?

- hartnn

you haven't posted question for b

- anonymous

If we randomly select a customer, what is the probability that she purchases a drink

- anonymous

sorry

- anonymous

?

- hartnn

can you make a venn diagram for your question ?

- anonymous

can you give me some idea?

- anonymous

|dw:1362261956915:dw|

- hartnn

yes^ from that can you find probability of drink ? just add all the values in D circle.

- anonymous

Makes you wonder what the last 25% are doing. Using the washroom or casing the joint.

- anonymous

0.35?

- anonymous

That looks good to me.

- hartnn

correct :)

- anonymous

awesome

- anonymous

t more quick questions

- anonymous

Which of the following statements is true?
G and D are independent.
G and C are independent.
C and D are independent.
None of the three pairs of events are independent.

- anonymous

You might want to go over how to do that diagram. That's a fundamental skill for these types of questions.

- anonymous

ok thanks

- anonymous

(d) Which of the following statements is true?
C and D are mutually exclusive.
G and D are mutually exclusive.
G and C are mutually exclusive.
None of the three pairs of events are mutually exclusive.

- hartnn

mutually exclusive events have intersection = 0 or if P(A and B)=0, then A, B are mutually exclusive.

- hartnn

so, do you find any such pair here ?

- anonymous

G and D are mutually exclusive.

- anonymous

?

- hartnn

G and D = 12+2 , its not 0

- anonymous

None of the three pairs of events are mutually exclusive.

- hartnn

yeah.

- anonymous

what about the previous one about independent?

- hartnn

for independent , P(A and B) = P(A)*P(B)
so, you need to check this for all 3 pairs.

- anonymous

pg and pd , i got 0.14

- hartnn

how ?

- anonymous

P(G or D)=0.61

- anonymous

Pg is 0.4

- anonymous

14% of customers purchase a gasoline and a drink
P（g and d）so it;s going to be 0.14

- hartnn

'or' ?? you need to use 'and'

- hartnn

P（g and d）so it;s going to be 0.14 is correct

- anonymous

so?

- anonymous

G and C we have 0.65

- hartnn

is that = p(g)*p(d) ??

- anonymous

oh no

- hartnn

then G and D are not independent.

- anonymous

0.144?

- hartnn

similar check for other 2 pairs.

- anonymous

why they are not independent?

- anonymous

0.216

- anonymous

so None of the three pairs of events are independent.

- hartnn

yeah

- anonymous

ok last question, i actually got the answer could you help me to check it?

- hartnn

yes?

- anonymous

What is P(C Dc), i.e., the probability that a randomly selected customer purchases cigarettes but not a drink?

- anonymous

i got 0.21

- hartnn

correct :)

- anonymous

thank you very much?

- hartnn

welcome?

- anonymous

wait

- anonymous

for this part

- anonymous

- anonymous

answer is not None of the three pairs of events are independent

- anonymous

?

- hartnn

i didn't calculate for all 3, but looking at numbers, i think its None...

- anonymous

yeah, but its not.

- anonymous

can you help me to check it please?

- hartnn

i still get none :(
lets have a 2nd opinion by @tcarroll010

- anonymous

help me on this one

- anonymous

- anonymous

im not sure, what are independent

- Mertsj

Independent means that the occurrence of one does not affect the probability of the other.

- Mertsj

Is there just one answer?

- anonymous

in this one, what are independent

- anonymous

yeah, they are multiple choice

- Mertsj

Then I guess I would choose G and C

- anonymous

why?

- anonymous

can you explain it?

- Mertsj

Because I can't see how one affects the other.

- anonymous

answer is wrong

- Mertsj

Do you get another chance?

- anonymous

yes last chance

- Mertsj

And you already tried "none"?

- anonymous

yes

- Mertsj

So it's a 50-50 chance. Let's see if we can pick out any difference in the two remaining choices.

- Mertsj

C & D don't mention the same commodity. If I had to guess, (and I would be guessing) that's what I would put.

- anonymous

my queststion is this

- anonymous

Which of the following statements is true?
G and D are independent.
G and C are independent.
C and D are independent.
None of the three pairs of events are independent

- anonymous

cuz , we are not sure

- bambimonster

Hey so what did u get in the end? Is it c and d

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