## yashar806 2 years ago 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

1. hartnn

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

2. hartnn

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

3. yashar806

0.04+0.36-?

4. hartnn

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

5. hartnn

9%

6. yashar806

what about P(A and B)

7. yashar806

oh I got it

8. hartnn

what you got as final answer ?

9. yashar806

what about b ?

10. hartnn

complete question ?

11. yashar806

i got 0.67

12. yashar806

is that right?

13. hartnn

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

14. yashar806

15. hartnn

you haven't posted question for b

16. yashar806

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

17. yashar806

sorry

18. yashar806

?

19. hartnn

can you make a venn diagram for your question ?

20. yashar806

can you give me some idea?

21. tcarroll010

|dw:1362261956915:dw|

22. hartnn

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

23. tcarroll010

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

24. yashar806

0.35?

25. tcarroll010

That looks good to me.

26. hartnn

correct :)

27. yashar806

awesome

28. yashar806

t more quick questions

29. yashar806

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.

30. tcarroll010

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

31. yashar806

ok thanks

32. yashar806

(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.

33. hartnn

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

34. hartnn

so, do you find any such pair here ?

35. yashar806

G and D are mutually exclusive.

36. yashar806

?

37. hartnn

G and D = 12+2 , its not 0

38. yashar806

None of the three pairs of events are mutually exclusive.

39. hartnn

yeah.

40. yashar806

what about the previous one about independent?

41. hartnn

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

42. yashar806

pg and pd , i got 0.14

43. hartnn

how ?

44. yashar806

P(G or D)=0.61

45. yashar806

Pg is 0.4

46. yashar806

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

47. hartnn

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

48. hartnn

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

49. yashar806

so?

50. yashar806

G and C we have 0.65

51. hartnn

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

52. yashar806

oh no

53. hartnn

then G and D are not independent.

54. yashar806

0.144?

55. hartnn

similar check for other 2 pairs.

56. yashar806

why they are not independent?

57. yashar806

0.216

58. yashar806

so None of the three pairs of events are independent.

59. hartnn

yeah

60. yashar806

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

61. hartnn

yes?

62. yashar806

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

63. yashar806

i got 0.21

64. hartnn

correct :)

65. yashar806

thank you very much?

66. hartnn

welcome?

67. yashar806

wait

68. yashar806

for this part

69. yashar806

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.

70. yashar806

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

71. yashar806

?

72. hartnn

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

73. yashar806

yeah, but its not.

74. yashar806

can you help me to check it please?

75. hartnn

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

76. yashar806

help me on this one

77. yashar806

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.

78. yashar806

im not sure, what are independent

79. Mertsj

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

80. Mertsj

Is there just one answer?

81. yashar806

in this one, what are independent

82. yashar806

yeah, they are multiple choice

83. Mertsj

Then I guess I would choose G and C

84. yashar806

why?

85. yashar806

can you explain it?

86. Mertsj

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

87. yashar806

88. Mertsj

Do you get another chance?

89. yashar806

yes last chance

90. Mertsj

And you already tried "none"?

91. yashar806

yes

92. Mertsj

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

93. 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.

94. yashar806

my queststion is this

95. yashar806

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

96. yashar806

cuz , we are not sure

97. bambimonster

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