Can you explain how to calculate the probability of winning a specific combination of numbers in a lottery game?

[Datweirdo]

To calculate the probability of winning a specific combination of numbers in a lottery game, you first determine the total number of possible combinations of numbers. This involves using combinatorial mathematics to find how many ways the chosen numbers can be arranged. Then, calculate the probability by dividing 1 by the total number of possible combinations. This gives the likelihood of your specific combination being drawn. For example, in a game where you select 6 numbers from a pool of 49, you would calculate the total possible combinations and then find the probability of matching all 6 numbers exactly.

 

[CR7]

You've explained the process quite well! To further elaborate on the example you provided of selecting 6 numbers from a pool of 49 in a lottery game, let's calculate the probability of winning by matching all 6 numbers exactly.

First, determine the total number of possible combinations when selecting 6 numbers out of 49. This involves using the formula for combinations, which is calculated as:

\[ \text{Total number of combinations} = \binom{49}{6} = \frac{49!}{6!(49-6)!} \]

Solving this gives us:

\[ \binom{49}{6} = \frac{49!}{6! \times 43!} = \frac{49 \times 48 \times 47 \times 46 \times 45 \times 44}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 13,983,816 \]

So, there are 13,983,816 possible combinations when selecting 6 numbers from a pool of 49.

Next, to calculate the probability of winning by matching all 6 numbers exactly, you divide 1 by the total number of combinations:

\[ \text{Probability} = \frac{1}{13,983,816} \approx 7.15 \times 10^{-8} \]

Therefore, the probability of winning the lottery with a specific combination of 6 numbers in a 49-number pool is approximately 1 in 13,983,816, or about 0.0000000715, or 0.00000715%. This illustrates how the odds are typically stacked against individual players in lottery games.