Chapter 6.5, Problem 63E

Consider the following events:

T = event that a randomly selected adult trusts credit card companies to safeguard his or her personal data

M = event that a randomly selected adult is between the ages of 19 and 36

O = event that a randomly selected adult is 37 or older

Based on a June 9, 2016, Gallup survey (“Data Security: Not a Big Concern for Millennials,” gallup.com, retrieved April 25, 2017), the following probability estimates are reasonable:

$P(T|M)=0.27P(T|O)=0.22$

Explain why P(T) is not just the average of the two given probabilities.