An article summarized data from a survey of a random sample of a certain number of U. S. adults with investments of $10,000 or more. Based on the survey data, it was estimated that 38.5% of investors manage their investments by doing everything they possibly can online. But the authors of the article also noted that there was quite a difference between younger investors (ages 18 to 49) and older investors (ages 50 and older). For younger investors, 63% said they do everything they possibly can online, while the percentage for older investors was 28%. A) Use the given information to estimate P(O), POLY), and P(OF) where 0 = event that a randomly selected Investor does everything possible online, Y = event that a randomly selected Investor is age 18 to 49, and F = event that a randomly selected investor is 50 years old or older.
B) Suppose that 40% of investors are between the ages of 18 and 49. Use the probabilities from part (a) and the estimate P(Y) = 0.40 to construct a hypothetical 1,000 table.
Y F Total
0
Not 0
Total 1,000
Use information in the table to calculate P(YO).
Which of the following sentences properly interprets this value in the context of this exercise?
A. The probability, given that a randomly selected investor is age 50 or older, that the investor does everything possible online is PLYO).
B. The probability, given that a randomly selected investor is age 18 to 49, that the investor does everything possible online is P(710).
C. The probability, given that a randomly selected investor does everything possible online, that the investor is age 50 or older is P(YO).
D. The probability, given that a randomly selected investor does everything possible online, that the investor is age 18 to 49 is Ayo).
E. The probability that the selected investor is age 18 to 49 is P(YO).