Suppose that in one area in California, 40% of all homeowners are insured against earthquake damage. Four homeowners are to be 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 3. There are 15 other outcomes.]
b. What is the most likely value for X?
c. What is the probability that at least two of the four selected have earthquake insurance?

Question

Quizplus · Accepted Answer

The Answer is a.

\begin{array} { l | l | l } \hline \mathrm { x } & ext { Outcomes } & P ( x ) \\hline 0 & ext { FFFF } & \1 & ext { FFFS, FFSF, FSFF, SFFF } & \2 & ext { FFSS, FSFS, SFFS, FSSF, SFSF, SSFF } & \3 & ext { FSSS, SFSS, SSFS, SSSF } & \4 & ext { SSSS } & \\hline\end{array}

b. P(x) is largest for x = 1 and 2
c. P(

X \geq 2

) = P(2) + P(3) + P(4) =.5248

Suppose That in One Area in California, 40% of All