Question: An analyst at a telephone marketing agency has studied the records of salespersons at a call centre over the past 5 years, and has concluded that the male telemarketers are more likely to make a sale than the females. He wishes to create a probability tree describing the possibilities when one marketing call is chosen at random. He defines various events as follows.

M: the marketer is a male,

F: the marketer is a female,

S: a sale is made,

\(\bar{S}\) : no sale is made.

The analyst observes that 60% of the calls were made by males. He further calculates some probabilities and adds them to the probability tree given below.

1. Add missing probabilities to the branches of the probability tree specifying the events
   clearly.
2. According to the tree diagram, what event probability is being represented by figure 0.12?
3. Find the probability that a sale is not made, given that the telemarketer is a male.
4. What is the probability that a sale is made and the telemarketer is a male?
5. Are the events "the caller is a female" and "a sale is made" independent?
6. Are the events "the caller is a female" and "the caller is a male" mutually exclusive?

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