Suppose that 30% of all homeowners in an earthquake-prone area of California are insured against earthquake...

Suppose that 30% 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 (.3)(.7)(.3)(.3) and associated x value of 3. There are 15 other outcomes.)

Value of x	Probability
0
1
2
3
4

(b) What is the most likely value of x?

0

1

1 and 0

3

4

(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) = ______

Expert Solution

a)

P(X=x)=

x	P(x)
0	0.2401
1	0.4116
2	0.2646
3	0.0756
4	0.0081

b) most likely value of x = 1

c)P (at least 2 of the 4 have earthquake insurance) = 0.2646+0.0756+0.0081 =0.3483

orchestra answered 3 years ago

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