In: Statistics and Probability
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) =
______
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