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

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 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 associated x value of 3. There are 15 other outcomes.)

Expert Solution

a) P(X = 0) = FFFF = 0.8 * 0.8 * 0.8 * 0.8 = 0.4096

P(X = 1) = SFFF + FSFF + FFSF + FFFS = 4 * 0.2 * 0.8 * 0.8 * 0.8 = 0.4096

P(X = 2) = SSFF + SFSF + SFFS + FFSS + FSFS + FSSF = 6 * 0.2 * 0.2 * 0.8 * 0.8 = 0.1536

P(X = 3) = SSSF + SSFS + SFSS + FSSS = 4 * 0.2 * 0.2 * 0.2 * 0.8 = 0.0256

P(X = 4) = SSSS = 0.2 * 0.2 * 0.2 * 0.2 = 0.0016

orchestra answered 2 years ago

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