The article “U.S. Investors Split Between Digital and Traditional Banking” (gallup.com, August 5, 2016, retrieved April 25, 2017) summarized data from a Gallup survey of a random sample of 1019 U.S. adults with investments of $10,000 or more.

Based on the survey data, it was estimated that 31% 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 (age 18 to 49) and older investors (age 50 and older). For younger investors, 43% said they do everything they possibly can online, while the percentage for older investors was 23%.

a. Use the given information to estimate P(O), P(O|Y), and P(O|F) where O = 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 calculate P(Y|O) and write a sentence interpreting this value.