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 four who have earthquake insurance. (a) Find the probahility 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 associated x value of 3. There are 15 other outcomes.) Probability (b) What is the most likely value of x? O 0 and 1 04 (c) What is the probability thal at least two of the four selected hoeowners have earthquake insurance? (at least 2 of the 4 have earthquake insurance)

Explanation / Answer

a)

x               P(x)

0               0.84 = 0.4096

1               4C1 * 0.21 * 0.83 = 0.4096

2               4C2 * 0.22 * 0.82 = 0.1536

3               4C3 * 0.23 * 0.81 = 0.0256

4               4C4 * 0.24 * 0.80 = 0.0016

b) Option-C) 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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