Suppose that 20% of all homeowners in an earthquake-prone area of California are

Question

Suppose that 20% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the rour who have earthquake insurance. (a) Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.2)(.8)(.2)(.2) and assaciated x value of 3. There are 15 other outcomes.) alue of x Probability (b) What is the most likely value of x? 0 and 1 (c) What is the probability that at least two of the four selected homeowners have earthquake insurance? P (at least 2 of the 4 have earthquake insurance) You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

Value of x                               Probability

0                                              0.4096

1                                              0.4096

2                                              0.1536

3                                              0.0256

4                                              0.0016

b) Most likely value of x is 0 and 1

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

                  = 0.1536 + 0.0256 + 0.0016 = 0.1808

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