Question

1. You perform an experiment and analyze three events A, B, and C. You decide that A is independent of Band B is independent of C. Must A be independent of C? If it’s always true, prove it. If it’s not always true, provide a situation where it would be false.

2. One of your friends likes buying scratch-off lottery tickets. One day, upon reading in the fine print that the probability that any given ticket is a winner is one in a thousand, he wistfully wishes aloud that he could afford one thousand tickets so that he could be sure to win.

a. What’s wrong with your friend’s logic? If he could buy a thousand tickets, what’s the probability he would win?

b. How many tickets would he have to buy to have a 90% chance of winning?

Answer 1

1. In our 3 expts A,B and C, if A is independent of B and B is independent of C, then it is not always true that A is independent of C. Consider Boyle Law in physics as an example, recording a certain pressure is independent of time, and recording a certain volume is also independent of time, however, the volume is a direct result of the pressure applied. Hence the relationship between A and C is indepedent of their relationship with B and the case described in the question is not always true