The word racecar and kayak are the same whether they are read left to right or right to left.

Puzzle #2027

Adam and his sister Florence had a pair of standard dice and were playing a game where each needed to throw a double to start. On his very first turn, Adam threw a double six.
1. How likely was Florence to throw a double six on her next throw?
2. How likely was she to throw any double on her next throw?
3. What were the chances of florence throwing, say, both a one and a six on her next throw?
4. How likely was she to throw her favorite number, four, on either of the die on her next throw?

1. There are six faces to each die, which could land any way up, thus the chance of throwing a double six is one in thirty-six.
2. There are six different combinations of doubles, thus the chance of throwing any double is six in thirty-six, i.e., one in six.
3. With six faces to each die, the chance of throwing one particular number is eleven in thirty-six. Throwing two dice does not double your chances of throwing a four, because if you have already thrown one, the second throw is irrelevant, so in one of your six tries you don't need to throw again, i.e., only in 5/6 of the times do you add the 1/6 chance of NOT throwing a four is 5/6 x 5/6, i.e., 25/36; thus the chance of throwing at least one four is 1-25/36, so 11/36.