The probability that a house in an urban area will beburglarized is 3%. If 45 ho

Question

The probability that a house in an urban area will beburglarized is 3%. If 45 houses are randomly selected what isthe probability that one of the houses will be burglarized? a. Is this a binomial experiment? Explain how youknow? b. Use the correct formula to find the probability thatout of 45 houses, exactly 3 of the houses will beburglarized. Show your calculations or explain how you foundthe probability. The probability that a house in an urban area will beburglarized is 3%. If 45 houses are randomly selected what isthe probability that one of the houses will be burglarized? a. Is this a binomial experiment? Explain how youknow? b. Use the correct formula to find the probability thatout of 45 houses, exactly 3 of the houses will beburglarized. Show your calculations or explain how you foundthe probability.

Explanation / Answer

p = 0.03, q = 1 - p = 0.97, n = 45;

P(1) = 45C1 0.03^1 0.97^44 =0.3534

(a) Yes. This is a binomial experiment becausethe probability of any house being burglarized is 3% or0.03

(b) We use the binomial formula: P(r) = nCr p^rq^(n - r)

P(3) = 45C3 0.03^3 0.97^42 =0.1066.

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