SOLUTION: A salesperson has a policy of calling upon a customer a second time if she does not make the sale on the first call, and trying a third time, and last time if she fails on the firs

Question 1042771: A salesperson has a policy of calling upon a customer a second time if she does not make the sale on the first call, and trying a third time, and last time if she fails on the first two calls. She has a probability of a sale on the first call of 0.3. If she fails on the first call, the probability of a sale on the second call is 0.2. If the first two calls are unsuccessful, her probability of success on the third call is only 0.1.
how i want do tree diagram for this question?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
A salesperson has a policy of calling upon a customer a second time if she does not make the sale on the first call, and trying a third time, and last time if she fails on the first two calls. She has a probability of a sale on the first call of 0.3. If she fails on the first call, the probability of a sale on the second call is 0.2. If the first two calls are unsuccessful, her probability of success on the third call is only 0.1.
how i want do tree diagram for this question?

Answer:
The tree diagram is shown below.
It is as important to understand how to interpret a tree-diagram as to draw it.
The probability of failure is the product of probabilities of all three steps, namely
P(failure)=0.7*0.8*0.9=0.504
The probability of success, however, is the sum of three possible cases, depending on the number of calls made.
P(success on first call)=0.3=0.300
P(success on second call)=0.7*0.2=0.140
P(success on third call)=0.7*0.8*0.1=0.056
So total probability of success
P(success)=0.300+0.140+0.056=0.496
which is complementary to P(failure), or
P(success)+P(failure)= 1.000
is a good check for the ansewr.

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