Question

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

Answer 1

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

Answer 2

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

Answer 3

0.04+0.36-?

Answer 4

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

Answer 5

9%

Answer 6

what about P(A and B)

Answer 7

oh I got it

Answer 8

what you got as final answer ?

Answer 9

what about b ?

Answer 10

complete question ?

Answer 11

i got 0.67

Answer 12

is that right?

Answer 13

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

Answer 14

what about b?

Answer 15

you haven't posted question for b

Answer 16

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

Answer 17

sorry

Answer 18

?

Answer 19

can you make a venn diagram for your question ?

Answer 20

can you give me some idea?

Answer 21

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

Answer 22

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

Answer 23

0.35?

Answer 24

That looks good to me.

Answer 25

correct :)

Answer 26

awesome

Answer 27

t more quick questions

Answer 28

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.

Answer 29

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

Answer 30

ok thanks

Answer 31

(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.

Answer 32

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

Answer 33

so, do you find any such pair here ?

Answer 34

G and D are mutually exclusive.

Answer 35

?

Answer 36

G and D = 12+2 , its not 0

Answer 37

None of the three pairs of events are mutually exclusive.

Answer 38

yeah.

Answer 39

what about the previous one about independent?

Answer 40

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

Answer 41

pg and pd , i got 0.14

Answer 42

how ?

Answer 43

P(G or D)=0.61

Answer 44

Pg is 0.4

Answer 45

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

Answer 46

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

Answer 47

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

Answer 48

so?

Answer 49

G and C we have 0.65

Answer 50

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

Answer 51

oh no

Answer 52

then G and D are not independent.

Answer 53

0.144?

Answer 54

similar check for other 2 pairs.

Answer 55

why they are not independent?

Answer 56

0.216

Answer 57

so None of the three pairs of events are independent.

Answer 58

yeah

Answer 59

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

Answer 60

yes?

Answer 61

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

Answer 62

i got 0.21

Answer 63

correct :)

Answer 64

thank you very much?

Answer 65

welcome?

Answer 66

wait

Answer 67

for this part

Answer 68

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.

Answer 69

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

Answer 70

?

Answer 71

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

Answer 72

yeah, but its not.

Answer 73

can you help me to check it please?

Answer 74

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

Answer 75

help me on this one

Answer 76

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.

Answer 77

im not sure, what are independent

Answer 78

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

Answer 79

Is there just one answer?

Answer 80

in this one, what are independent

Answer 81

yeah, they are multiple choice

Answer 82

Then I guess I would choose G and C