c) A certain Mobile Money Agency is an agent for Zanaco Express, Airtel, MTN and Zamtel Mobile Money. Experience has shown that the probabilities of finding a float for withdrawals of amounts K5000 and above are given as 0.4, 0.5, 0.3 and 0.2, respectively. Experience has also shown that among his clients, the probabilities that a client requires a service from Zanaco Express, Airtel, MTN, Zamtel Mobile Money are given as 0.3, 0.4, 0.2 and 0.1, respec- tively. Assume that each client visits the agency for withdrawals from only one at a time.
(i) What is the probability that a client who wishes to withdraw K5000 will not be successful?
[3 marks]
(ii) What is the probability that an MTN client who wishes to withdraw K5000 will not be successful?
[2 marks]
(iii) What is the probability that an Airtel client who wishes to withdraw K5000 will not be successful?
[2 marks]
(iv) A certain client has just failed to make a withdrawal of K7000, what is the probability that he/she is a Zamtel Mobile money client?
Consider the following events:
D: withdraw k5000 will not be successful,
ZE: a service from Zanaco Express,
A: a service from Airtel,
MTN: a service from MTN,
ZMM: a service from zamtel mobile money.
i) By the Law of Total Probability
"P(D)=P(ZE)P(D|ZE)+P(A)P(D|A)"
"+P(MTN)P(D|MTN)+P(ZMM)P(D|ZMM)"
"=0.3(1-0.4)+0.4(1-0.5)+0.2(1-0.3)"
"+0.1(1-0.2)=0.6"
ii)
iii)
iv) By Bayes' Theorem
"=\\dfrac{(1-0.2)(0.1)}{0.6}=\\dfrac{2}{15}\\approx0.1333"
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