If two dice are thrown what is the probability of the sum of the numbers being a seven or an eleven?

Answer 1

To roll a 7, it doesn't matter what your first die rolls at, as every number on the die has a complement that will add up to 7. This means that your odds on rolling 7 are actually your odds on rolling the appropriate number on the second die. ie. 1/6. No matter what your first die is, the second can potentially give you a number that brings the total to 7.

To roll an 11 however, your odds are not as high. This is because you must roll a five and a six to hit 11. Your first die can be either of the two, but your second die must be it's complement. In this case then, your odds are 2/6 * 1/6, or 1/18.