Question 1: In front of you are four cards. You know that each card has a photo of a famous person on one side, and a photo of an animal on the other. The four sides that are visible to you are as follows: Ken Ham, Richard Dawkins, a narwhal, and a T-Rex. I let you know that all of these cards follow the same rule - that if a card has a religious person on it's famous person side, it has a dinosaur on its animal side. What's the lowest number of cards you'd need to flip to determine if this rule is true or false for these cards, and which cards would you flip?
Answer from UrsaMinor: "You would have to flip two cards to test the rule. If it is true, Ken Ham will have a dinosaur on the reverse, and the narwhal will have a non-religious person on the reverse. Since there is no rule stating that non-religious people must have any particular theme on the reverse, it is not necessary to turn over the Richard Dawkins and T-Rex cards, because no matter what they have on the reverse sides, they cannot not break the rule."
Alternative smartass answer from James F. McGrath: "Question 1 is a trick question to prevent banana-wielding creationists from winning. Anyone who embraces mainstream science will know that the categories "famous persons" and "animals" overlap. :)"
Question 2: Because I'm super nice, I give you a giant one hundred pound watermelon as a gift. You determine that this giant watermelon is ninety-nine percent water by weight. Unfortunately you let the watermelon sit out in the sun, and some water evaporates. Now the watermelon is only ninety-eight percent water by weight. To the nearest pound, what does the watermelon now weigh?
Answer from Gary Usleaman: "This one was fun! Since it started out at 100 lbs. and 99% water, then that means that 1% (or 1 lb) was Not Water (NW). After letting it rot in the sun for a bit (best thing for water mellon, if you ask me), you find that it is 98% water. [BTW, you had to weigh it to figure that out anyway, so why are you asking me how much it weighed?] Well, the 1 lb of NW didn't change, so that means that 1 lb is 2% of the total weight. That makes the total weight 50 lbs."
Question 3: While you were at TAM9, you decided to suspend skepticism and gamble - specifically, by playing roulette. But since you want to have some sort of strategy, you decide to flip a coin before each bet to decide whether to place a bet on red or on black (which should have a 50/50 chance of happening). Sadly, you lose sixty seven times in a row - that is, the ball always lands on the opposite color that you pick. If you turned your skepticism back on, it would be most rational to think:
A. You just have shitty luck
B. It's terrible strategy to flip a coin to pick what color to bet on in roulette
C. You should keep up this strategy because you've really likely to win the next bet
D. The roulette table is obviously broken, but you can't assume that's intentional
E. The casino or the staff are dirty crooks who have rigged the game against you somehow
F. You can't reasonably decide which of the listed options are more likely
Answer from Jonathan: "The probability of losing 67 times in a row is one in 2^67, ie about 1 in 147 billion billion. So this is *extremely* unlikely to be bad luck. If the game is fair, flipping a coin is no worse than any other strategy - there's no pattern to pick up on. C is for idiots, D might make sense if you were always betting (say) red, but since your choice is random and there's no sensible way your coin toss can directly affect the wheel, if must be E, and the casino is seeing your bet, then manipulating the wheel (or, at least, it's far more likely that the casino is crooked than that you've lost fairly 67 times on the trot)."
Katie was nice enough to make up some graphs of your responses:
Most of you guessed I would fail at the door question, followed by the roulette question... But I actually got the watermelon question wrong. I know, I know. The answer is obvious now that I see it, but I'm rusty and wasn't thinking. Alas.
Congrats to our winner, Jimmyrhoffa, who was the first to get all of these right! Katie should have your prize to you soon.