Some parts of California are particularly earthquake-prone. Suppose that in one such area, 31% of all homes are built to withstand a 9.0 magnitude earthquake. Four homes are to be selected at random. Let Xdenote the number among the four that can withstand a level 9.0 magnitude earthquake. Let S denote a home that can withstand a 9.0 magnitude earthquake and F one that can not. Then one possible outcome is SFSS, with probability (0.31)(0.69)(0.31)(0.31) and associated X value 3.
(a) What is the minimum possible value of X?
(b) What is the maximum possible value of X?
(c) Find X for all possible outcomes. (16 of them) Find the probability distribution of X.
(d) What is the most likely value for X?
(e) What is the probability that at least two of the four selected can withstand a magnitude 9.0 earthquake?