Short Answer 
Lottery systems, like a 5/90 lottery, operate on randomness, making it impossible to predict future winning numbers. To evaluate whether playing is worthwhile, players can use the expected gain formula, which considers the probability of winning multiplied by the prize value. Additionally, each draw is considered an independent event, reinforcing the unpredictability of outcomes.
Step 1: Understand Lottery Randomness
Lottery systems, such as a 5/90 lottery, operate based on randomness. This means that each number drawn has an equal chance of being selected at every draw, regardless of the outcomes of previous draws. Consequently, there is no reliable way to predict which numbers will be drawn in the future.
Step 2: Use the Expected Gain Formula
The key formula to evaluate the value proposition of playing a lottery is: expected gain = probability of winning x value of prize. This calculation helps players determine if the ticket price is justified based on the potential rewards. It is important to note that this formula is not used to predict specific winning numbers.
Step 3: Recognize Independent Events
In a 5/90 lottery, the probability of selecting all five numbers correctly relies on the concept of independent events. Each draw does not affect the next, meaning that previous outcomes do not influence future draws. Therefore, understanding this independence emphasizes the unpredictability of the winning numbers.