Chapter 6.4, Problem 36E

The newspaper article “Folic Acid Might Reduce Risk of Down Syndrome” (USA TODAY, September 29, 1999) makes the following statement: “Older women are at a greater risk of giving birth to a baby with Down Syndrome than are younger women. But younger women are more fertile, so most children with Down Syndrome are born to mothers under 30.”

Let D = event that a randomly selected baby is born with Down Syndrome and Y = event that a randomly selected baby is born to a young mother (under age 30). For each of the following probability statements, indicate whether the statement is consistent with the quote from the article, and if not, explain why not.

1. a. P(D|Y) = 0.001, P(D|Y^C) = 0.004, P(Y) = 0.7
2. b. P(D|Y) = 0.001, P(D|Y^C) = 0.001, P(Y) = 0.7
3. c. P(D|Y) = 0.004, P(D|Y^C) = 0.004, P(Y) = 0.7
4. d. P(D|Y) = 0.001, P(D|Y^C) = 0.004, P(Y) = 0.4
5. e. P(D|Y) = 0.001, P(D|Y^C) = 0.001, P(Y) = 0.4
6. f. P(D|Y) = 0.004, P(D|Y^C) = 0.004, P(Y) = 0.4