Some parts of Caromia are particularly earthquake-prone. Suppose that in one met

Question

Some parts of Caromia are particularly earthquake-prone. Suppose that in one metropolitan area 28% of a carthquake Insurancs. homeowners are insured against earthquake da eqe. Four homeowners are to be selected at randam Let X denate he number a on the rour who have (a) Find the probabiity distibution ofx. [hint: Let S denote a homeowner that has insurance and Fone who dbes not. Then one possible outcome is SSS, with probability (0.2810.72)00.28)00.23y and associated X va ue 3. There are 15 other outcomes.] Raund your answers to faur decimal places.) () 0.269x b)Draw the corresponding prcbatility histogram. Probabliy 0.3 0.3 0.2 0,1 0.2 Number with Number with Probabliry Probability 04 03 0.2 0.2 Number with 0.1 Number with c) What is the most lkcly valuc for Xt d) what is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four deciml places.)

Explanation / Answer

a) p = 0.26

n = 4

P(X = 0) = 4C0 * 0.260 * 0.744 = 0.2999

P(X = 1) = 4C1 * 0.261 * 0.743 = 0.4214

P(X = 2) = 4C2 * 0.262 * 0.742 = 0.2221

P(X = 3) = 4C3 * 0.263 * 0.741 = 0.0520

P(X = 4) = 4C4 * 0.264 * 0.740 = 0.0046

b) Option-A) is the correct graph

c) Most likely value for X is 1.

d) P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4)

                  = 0.2221 + 0.0520 + 0.0046

                  = 0.2787

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