Question 1178011
Here's how to calculate the expected value of the lottery game:

**1. Calculate the Total Number of Combinations**

* We need to find the number of ways to choose 6 numbers from 30, where order doesn't matter. This is a combination problem, denoted as "30 choose 6" or C(30, 6).
* C(30, 6) = 30! / (6! * 24!) = 593,775

**2. Calculate the Probability of Winning**

* There's only one winning combination.
* The probability of winning is 1 / 593,775.

**3. Calculate the Probability of Losing**

* The probability of losing is 1 - (probability of winning).
* Probability of losing = 1 - (1 / 593,775) = 593,774 / 593,775.

**4. Calculate the Expected Value**

* Expected value = (probability of winning * winnings) + (probability of losing * loss)
* Expected value = (1 / 593,775 * $40,000) + (593,774 / 593,775 * -$1)
* Expected value = (40,000 / 593,775) - (593,774 / 593,775)
* Expected value = (40,000 - 593,774) / 593,775
* Expected value = -553,774 / 593,775
* Expected value ≈ -$0.9326

**Therefore, the expected value of this game is approximately -$0.93. This means that on average, a player can expect to lose about $0.93 for each ticket they buy.**