Chances: Risk and Odds in Everyday Life , by James Burke, reports that the proba

Question

Chances: Risk and Odds in Everyday Life, by James Burke, reports that the probability of a police officer will be killed in the line of duty is 0.90% (or less).

1. What is the probability that no officer in this precinct will be killed in the line of duty? (Use 4 decimal places.)
2. What is the probability that one or more officers in this precinct will be killed in the line of duty? (Use 4 decimal places.)

3. What is the probability that two or more officers in this precinct will be killed in the line of duty? (Use 4 decimal places.)

Explanation / Answer

it will be solved by taking it to be poisson distribution with lambda = 0.9

a) p(x=0) = 0.9^0*e^(-0.9)/0.9! = 0.4065

b) p(x>=1) = 1 - p(x=0) = 1-0.4065 = 0.5935

c) here we need to find p(x>=2) = 1 - p(0) - p(1)

p(1) = 0.9^1*e^(-0.9)/1! = 0.3659

therefore p(x>=2) = 1 - 0.5935 - 0.3659 = 0.0406

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