# Nine paradoxes with a statistical theme

Questions

1. A drill sergeant always yells at one of his trainees when she messes up. The drill sergeant notices that after he yells at her, her performance improves. Later it turns out that the trainee is deaf, blind, and has no other way of actually noticing that drill sergeant is yelling at her. Ignoring the effect of practice, why might the trainee’s performance have improved anyway?
2. You have 100 pounds of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water by weight. How much do they weigh now and why?
3. Imagine that your parents had rolled a six-sided die to decide how many children to have. What did they most likely roll and why?
4. You have access to planes that have returned from military missions and the distribution of the bullet “wounds” on the planes. Which areas should you recommend to have extra armor?
5. Why would few people choose to play in a lottery with a small but actual probability of success with an infinite monetary expected value?
6. Do most people have have the same, more, or fewer friends than their friends have on average and why?
7. Hypothetically, say that 80% of people dream in color, and 68% of sexual partners have the same (concordant) coloring of their dreams. If you dream in color, what’s the probability that your partner will too?
8. Are we biased to think that cars in the lanes next to us are going faster or slower than they really are and why?
9. Why is the expression “the smallest positive integer not nameable in under eleven words” paradoxical?