Question 998749: Based on the following results from a recent survey for a telecommunication company, would you say that it is equally likely for customers of this company to access customer service through each of the four different channels? In terms of customer service, what is the implication for the company from a staffing perspective?
Channel Preferred choice for customer service
1-800 number to the call centre 345
Email 216
Online Chat 84
Visit to a store 143
What is wrong with the following statements? Please explain.
a. P(A) = -0.3
b. P(Ac)=0.6 given that P(A) = 0.3
c. P(A or B) = 0.7 if P(A) =0.4 and P(B) =0.3
d. P(A and B) is always greater than 0
Given that P(A)=0.64, P(B)=0.42 and P(A and B) = 0.3, calculate the following:
a. P(Bc)
b. P(A or B)
c. P(the complement of the event “A and B”)
d. P(A|B)
e. P(B|A)
f. Are Events A and B independent? Please use probabilities to justify your answer.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first part to get you started
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What is wrong with the following statements? Please explain.
a. P(A) = -0.3
b. P(Ac)=0.6 given that P(A) = 0.3
c. P(A or B) = 0.7 if P(A) =0.4 and P(B) =0.3
d. P(A and B) is always greater than 0
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a)
You cannot have a negative probability. The probability MUST be between 0 and 1 (inclusive).
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b)
P(A^c) + P(A) = 1 is always true. But notice how 0.6 and 0.3 do not add to 1. So we have a contradiction here. If P(A^c) = 0.6, then P(A) = 0.4. Or if P(A) = 0.3, then P(A^c) = 0.7
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c)
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A)*P(B) ... assuming A and B are independent
P(A or B) = 0.4 + 0.3 - 0.4*0.3
P(A or B) = 0.7 - 0.12
P(A or B) = 0.58
So P(A or B) should equal 0.58. P(A or B) is only equal to 0.7 IF events A and B are mutually exclusive. I.e. when P(A and B) = 0
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d)
The statement "P(A and B) is always greater than 0 " is false because it is possible for P(A and B) to be equal to zero. It is possible for events A and B to be mutually exclusive. Two events are mutually exclusive when they cannot happen at the same time.
Example:
Event A: Rolling a 5 on a single die
Event B: Rolling a 6 on a single die (same die as event A)
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