the following probability model shows the distrubiton of family structure among
ID: 3337990 • Letter: T
Question
the following probability model shows the distrubiton of family structure among families with at least one child younger than 18 years of age in 2013: Two married parents, first marriage; probabilty is 0.46. Two married parents, one or both remarried; probability is 0.15. Single parent; probability is 0.34. No parent at home; probability is 0.05. (A) Verify that this is a probability model. (B) What is the probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had two married parents in their first marriage? Interpret the probability. (C) What is the probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had two married parents? Interpret the probability. (D) What is the probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had at least one parent at home? Interpret this probability.
Explanation / Answer
a) It will be a model if sum = 1
So, P = 0.46 + 0.34 + 0.15 + 0.05 = 1
b) The probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had two married parents in their first marriage = 0.46
It tells us that 46% of families had had two married parents in their first marriage with at least one child younger than 18 years of age in 2013.
c) The probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had two married parents = 0.46 + 0.15 = 0.61
It tells us that 61% of families had had two married parents with at least one child younger than 18 years of age in 2013.
d) The probability that a randomly selected family with at least one child younger than 18 years of age in 2013 had at least one parent at home = 0.46 + 0.15 + 0.34 = 0.95
It tells us that 95% of families had at least one parent at home with at least one child younger than 18 years of age in 2013.
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