Find the probability that in one call she sells no magazines.
A telemarketer sells magazine subscriptions over the telephone. The probability of a busy signal or no answer is 65%. If the telemarket does make contact, the probability of 0,1,2, or 3 magazine subscriptions is .5,.25,.20, .05, respectively.
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This probability question uses something called conditional probability (see link below). We have two situations in which she sells no magazines:
1) She is unable to make contact (probability = 0.65)
2) She makes contact, but is unable to sell anything. (probability explained below).
The probability she sells nothing given that she makes contact is 0.5. However, because this is a conditional probability, we have to multiply this by the probability that she is able to make contact (0.35). In other words, the probability of Case 2 is the probability that she make contact AND that she sells nothing given that she makes contact.
Now, considering that either one of these cases can happen to satisfy the condition that the telemarketer sell nothing, we can simply add the two probabilities as if they were independent events!
Let's let `P(N)` be the probability she sells nothing, and `P_1` and `P_2` be the probabilities for cases 1 and 2, respectively.
`P(N) = P_1+P_2=0.65 + 0.35(0.5) = 0.65+0.175 = 0.825`
So, she has an 82.5% probability of selling nothing on each phone call.
I hope that helps!
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