# Problem of the Day: 2/17/13

In the figure below, PQSR is a square with side length 3 inches, and RT is 5 inches. What is the length of the lower segment of QS?

Solution to yesterday’s problem:

We need to find the two parts of the probability: the total number of possible occurrences and the number of occurrences that satisfy our conditions. We can find the first number using the blanks method. There are two dice, so there are two blanks:

____ ____

There are six possibilities for both the first and second dice:

__6__ __6__

So there are 36 possibilities. However, we need to divide by 2 because there are two possibilities listed for each desired possibility; for instance, 2 and 4 is listed as 2 and 4 and 4 and 2. Finally the first number in the probability is 18.

For the second number, we count the number of combinations whose difference is 2. This is quite simply 1 and 3, 2 and 4, 3 and 5, and 4 and 6. So the second number is 4. Simplifying the probability, we find an answer of 2/9.