In a lottery game, a player picks 7 numbers from 1 to 45 . If 6 of the 7 numbers match those drawn, the player wins second prize. What is the probability of winning this prize? Be sure to leave your answer as a fraction in order to earn credit.

There is a probability of winning second prize.

Hint: The chances of winning are the total ways you can pick 6 out of 7 numbers divided by the number of ways you can pick 7 numbers out of 45 .

Step 1 ：In a lottery game, a player picks 7 numbers from 1 to 45. If 6 of the 7 numbers match those drawn, the player wins second prize. We are asked to find the probability of winning this prize.

Step 2 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the total number of outcomes is the number of ways we can pick 7 numbers out of 45. The number of favorable outcomes is the number of ways we can pick 6 out of these 7 numbers.

Step 3 ：We can calculate these using combinations. The formula for combinations is \(nCr = \frac{n!}{r!(n-r)!}\), where \(n\) is the total number of items, \(r\) is the number of items to choose, and \(!\) denotes factorial.

Step 4 ：Using this formula, we find that the total number of outcomes is \(45C7 = 45379620\).

Step 5 ：The number of favorable outcomes is the number of ways we can pick 6 out of these 7 numbers, which is \(7C6 = 7\). However, we also need to account for the one number that was not drawn. There are 38 possibilities for this number (the 45 total numbers minus the 7 chosen), so the total number of favorable outcomes is \(7 \times 38 = 266\).

Step 6 ：Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. This gives us \(\frac{266}{45379620} = 5.8616621293875975e-06\).

Step 7 ：Final Answer: The probability of winning the second prize is \(\boxed{\frac{266}{45379620}}\) or approximately \(\boxed{5.8616621293875975e-06}\).