yashar806
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
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hartnn
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P(A or B) = P(A)+ P(B)-P(A and B)
here, A = gasoline, B =cigarette
hartnn
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you know all 3, P(A),P(B),P(A and B)
just plug in values!
yashar806
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0.04+0.36-?
hartnn
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40% = 0.4
and P(G and C) is given as % = 0.09
hartnn
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9%
yashar806
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what about P(A and B)
yashar806
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oh I got it
hartnn
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what you got as final answer ?
yashar806
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what about b ?
hartnn
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complete question ?
yashar806
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i got 0.67
yashar806
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is that right?
hartnn
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lets check,
P(G or C) = 0.4+0.36-0.09 = 0.76-0.09 = 0.67
yes, you are correct :)
yashar806
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what about b?
hartnn
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you haven't posted question for b
yashar806
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If we randomly select a customer, what is the probability that she purchases a drink
yashar806
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sorry
yashar806
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?
hartnn
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can you make a venn diagram for your question ?
yashar806
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can you give me some idea?
tcarroll010
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|dw:1362261956915:dw|
hartnn
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yes^ from that can you find probability of drink ? just add all the values in D circle.
tcarroll010
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Makes you wonder what the last 25% are doing. Using the washroom or casing the joint.
yashar806
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0.35?
tcarroll010
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That looks good to me.
hartnn
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correct :)
yashar806
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awesome
yashar806
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t more quick questions
yashar806
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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.
tcarroll010
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You might want to go over how to do that diagram. That's a fundamental skill for these types of questions.
yashar806
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ok thanks
yashar806
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(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
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mutually exclusive events have intersection = 0 or if P(A and B)=0, then A, B are mutually exclusive.
hartnn
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so, do you find any such pair here ?
yashar806
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G and D are mutually exclusive.
yashar806
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?
hartnn
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G and D = 12+2 , its not 0
yashar806
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None of the three pairs of events are mutually exclusive.
hartnn
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yeah.
yashar806
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what about the previous one about independent?
hartnn
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for independent , P(A and B) = P(A)*P(B)
so, you need to check this for all 3 pairs.
yashar806
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pg and pd , i got 0.14
hartnn
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how ?
yashar806
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P(G or D)=0.61
yashar806
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Pg is 0.4
yashar806
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14% of customers purchase a gasoline and a drink
P（g and d）so it;s going to be 0.14
hartnn
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'or' ?? you need to use 'and'
hartnn
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P（g and d）so it;s going to be 0.14 is correct
yashar806
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so?
yashar806
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G and C we have 0.65
hartnn
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is that = p(g)*p(d) ??
yashar806
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oh no
hartnn
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then G and D are not independent.
yashar806
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0.144?
hartnn
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similar check for other 2 pairs.
yashar806
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why they are not independent?
yashar806
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0.216
yashar806
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so None of the three pairs of events are independent.
hartnn
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yeah
yashar806
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ok last question, i actually got the answer could you help me to check it?
hartnn
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yes?
yashar806
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What is P(C Dc), i.e., the probability that a randomly selected customer purchases cigarettes but not a drink?
yashar806
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i got 0.21
hartnn
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correct :)
yashar806
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thank you very much?
hartnn
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welcome?
yashar806
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wait
yashar806
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for this part
yashar806
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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.
yashar806
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answer is not None of the three pairs of events are independent
yashar806
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?
hartnn
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i didn't calculate for all 3, but looking at numbers, i think its None...
yashar806
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yeah, but its not.
yashar806
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can you help me to check it please?
hartnn
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i still get none :(
lets have a 2nd opinion by @tcarroll010
yashar806
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help me on this one
yashar806
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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.
yashar806
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im not sure, what are independent
Mertsj
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Independent means that the occurrence of one does not affect the probability of the other.
Mertsj
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Is there just one answer?
yashar806
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in this one, what are independent
yashar806
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yeah, they are multiple choice
Mertsj
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Then I guess I would choose G and C
yashar806
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why?
yashar806
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can you explain it?
Mertsj
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Because I can't see how one affects the other.
yashar806
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answer is wrong
Mertsj
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Do you get another chance?
yashar806
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yes last chance
Mertsj
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And you already tried "none"?
yashar806
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yes
Mertsj
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So it's a 50-50 chance. Let's see if we can pick out any difference in the two remaining choices.
Mertsj
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C & D don't mention the same commodity. If I had to guess, (and I would be guessing) that's what I would put.
yashar806
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my queststion is this
yashar806
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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
yashar806
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cuz , we are not sure
bambimonster
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Hey so what did u get in the end? Is it c and d