7. Some More Riddles (cont.)

1. Rolling dice
Q - If you roll a two 6-sided dice, what are the odds will get least one 3?
A - There is an 11 in 36 chance that you a roll of two dice will result in one 3.
(NB most people will think the odds are 1 in 3. This is incorrect and is best explained by reframing the question, ie what are the chances of not rolling a 3 with two dice?)
2. Coins
Q - There are 10 coins; each differently weighted. One is normal, evenly weighted coin. The other 9 coins are all unevenly weighted, though no two in exactly the same way, ie some are weighted to land more often on heads and some on tails. You are given 30 minutes to flip a coin you wish; you will be allowed to flip 100 times in total. For every head you flip, you win a point. How do you go about the process to maximise points?
A - Pick an unevenly weighted coin and flip it until it comes up tails; based on how many flips that took, decide whether to proceed with the coin or move on to another one.
3. Basketball
Q. What are the odds that you have a relative who is a professional basketball player?
A. 1  in 50
(NB need to check out the definitions for a relative and a professional player)
These 3 riddles are designed to test blindspots in your mind plus testing your understanding of information: when you sought it, how you sought it, how you updated your beliefs and respond to it
(source: Michael Lewis, 2023)