Final answer:
The probability of matching the winning lottery numbers when choosing 6 different numbers from a set of 13 is 1 out of 1716 combinations, or approximately 0.00058207.
Step-by-step explanation:
To calculate the probability of matching all six winning numbers in a lottery where 6 different numbers are drawn at random from a set of 13, we use combinations since the order of the numbers does not matter. The total number of possible combinations for choosing 6 numbers out of 13 is determined by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.
In this case, for n=13 and k=6, the total number of combinations is C(13, 6) = 13! / (6!7!) = 1716. This is the number of all possible sets of 6 numbers that can be drawn. Since there is only one set of winning numbers, the probability of choosing that one set is 1 out of 1716, or P(winning) = 1/1716.
So, the probability that you will match the winning numbers is 1/1716, or approximately 0.00058207.