Question: You have three coins. One always comes up heads, one always comes up tails, and one is just a regular coin (has equal change of heads or tails). If you pick one of the coins randomly and flip it twice and get heads twice, what is the chance of flipping heads again?
Answer: 90 percent. If you pick the heads coin the chance of getting the first 2 heads is 100 percent (4/4) and if you pick the fair coin the chance is 25 percent (1/4). So from this, the chance that it is the heads coin is 4/5 and the fair coin 1/5.
Then, if it is the heads coin you will definitely get heads (4/5). If you flip the fair coin it is 1/10 (1/5 * 1/2). Add the probabilities together: 4/5 + 1/10 = 9/10.
Question: Your friend tells you about a story he once tried to impress a young lady with, but instead got a slap in the face. He wants you to attempt to see the flaw: It was a hot and windless day, in our bunker, when suddenly one of ours yelled: "Enemy!" We opened fire on them, leaving one hundred of them dead before they retreated. I was checking a dead captain's glasses when the shout came that they were incoming again, and the CO ordered us to open up on them with our mortars, when I yelled: "Cease fire! They're Americans!" Later, an American colonel thanked me for my work after I said that I saw their flag, waving back and forth in the wind. What is wrong with this story?
Answer: At the beginning, it was said that "It was a hot and windless day," yet at the end, it is said that "The flag was waving back and forth". Had it been windless, the flag would have been limp.
Question: Your father is a scientist who has invented a red pill which, if eaten with 1 blue pill which he has invented, will grant immortality. The night he invents it, he gives you 2 red and 2 blue pills just in case one of them is lost or substandard. He also warns you that an overdose will cause the opposite effect and kill you instead. You put the pills in your pocket and leave his lab for home. On the way home, you are abducted by aliens who blindfold you and throw you into a singularity. At this point, you remember the pills your father gave you. You take them out (you can move and have enough oxygen in space for a short time), but realize that you can't tell the red pill from the blue pill. Even if you take off your blindfold, you can't see anything due to your proximity to the black hole. Given the circumstances, how do you successfully eat 1 red and 1 blue pill and survive?
Answer: Eat half of each pill.