A person receives one gold coin everyday and each gold coin

A person receives one gold coin everyday and each gold coin might be a counterfeit with probability 0.2. What is the probability that the first counterfiet is received on the 4th day? What is the probability that the first counterfiet is received in the first 3 days? When (on which day) does this person expect to receive the first couterfiet?

Solution

a)

P = (0.8^4)*(0.2) = 0.08192 [ANSWER]

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b)

P = P(1st day) + P(2nd day) + P(3rd day)

= 0.2 + 0.8*0.2 + 0.8^2*0.2

= 0.488 [ANSWER]

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c)

E(x) = 1/p = 1/0.2 = 5th day [ANSWER]