1.You test positive for a disease that occurs in 1% of the population and are told that the test is 95% accurate. What is the probability that you actually have the disease?
2.A simple game: Two people are chosen at random and are asked to take out their wallets and count the cash. Whoever has more cash must give it to the other player.
Suppose that you are selected and asked if you want to play. You have no idea of who the other person is but argue like this: "If I have more money, I will lose what I have. However, if I have less money, I will win more than what I have. It seems that I can expect a gain in this game so I will definitely play." But then you see the smug look on your opponent's face and realize that (s)he has gone through the exact same reasoning and concluded that the game is in her/his favor. Can the game really be favorable to both of you???
Obviously not, and here is why.
3.The Old Faithful geyser in Yellowstone National Park erupts on average once every 90 minutes. If you arrive at random, you would expect to wait on average 45 minutes for the next eruption. However, after repeated random arrvals, you notice that your average wait is more than 45 minutes. Bad luck?
Not at all. There is a perfectly logical explanation.