In the "Magical Six" TV contest, players multiply their prize if they roll a six with one of the two dice or if the sum of the numbers rolled is 6. What is the probability that a player will multiply their prize?
With two dice, we have a total of $6 \cdot 6=36$ different possible outcomes. Among these, the favorable outcomes are those where a six is rolled, or the sum of the points rolled is 6. Let's calculate how many such outcomes are possible.

A) A six is rolled on both dice, which is one possibility.

B) A six is rolled on one die, and the other die shows one of the numbers $1,2,3,4,5$; this results in a total of 10 possibilities.

C) The sum of the numbers on the two dice can be 6 in five different ways: $(1 ; 5)(2 ; 4)(3 ; 3)(4 ; 2)(5 ; 1)$.

Therefore, the number of favorable outcomes is: $1+10+5=16$.

The probability of an event is obtained by dividing the number of favorable outcomes by the total number of outcomes, in our case $p=\frac{16}{36}=\frac{4}{9}$.