(e) What is the probability that at least two of the four selected can withstand
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Question
(e) What is the probability that at least two of the four selected can withstand a magnitude 9.0 earthquake?
Some parts of California are particularly earthquake-prone. Suppose that in one such area, 30% of all homes are built to withstand a 9.0 magnitude earthquake. Four homes are to be selected at random. Let X denote 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 (0.30) (0.7) (0.30) (0.30) 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. Outcome SSSS SSSF SSFS SSFF SFSS SFSF SFFS SFFF Outcome FSSS FSSF FSFS FSFF FFSS FFSF FFFS Find the probability distribution of X 0 (d) What is the most likely value for X?Explanation / Answer
c)
Outcome X
SSSS 4
SSSF 3
SSFS 3
SSFF 2
SFSS 3
SFSF 2
SFFS 2
SFFF 1
FSSS 3
FSSF 2
FSFS 2
FSFF 1
FFSS 2
FFSF 1
FFFS 1
FFFF 0
X P(X)
0 0.74 = 0.2401
1 4 * 0.73 * 0.3 = 0.4116
2 6 * 0.72 * 0.32 = 0.2646
3 4 * 0.7 * 0.33 = 0.0756
4 0.34 = 0.0081
d) Most likely value for X is 1.
e) P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2646 + 0.0756 + 0.0081 = 0.3483
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