Here's a question:
Say that there is a 1/2 chance of winning one dollar in a lottery.
Let's say that a woman buys two tickets, thinking that one of them will win because of the odds. Both tickets lose.
Why?
Because:
Lottery odds (and most other odds) are NOT RELATED EVENTS.
What are related events?
Related events are events that influence each other.
In short, it DOES NOT MATTER what happened with the first ticket, because the two tickets are independent, and do not rely on each other to change the odds.
Here's another way to look at it:
Let's say that there are three marbles in a box. One red, one blue, and one green. Now, you are trying to pull out a blue marble without looking. If you do NOT pull out a blue marble, you keep the marble you have drawn out. Here are the odds of these events.
1st Try: 1/3
2nd Try: 2/3
3rd Try: 3/3 (1/1)
These are related events. One's result directly affects the next result.
Now, let's say that you put the marble BACK in if you do not retrieve blue. Then the odds are:
1st Try: 1/3
2nd Try: 1/3
3rd Try: 1/3
These events are unrelated. You could pull out the marbles ten times, and still not get the blue marble.
However, better odds DO have an effect on unrelated events. It is much harder to get a single blue marble within 100 red marbles.
In conclusion, ALWAYS make sure you know whether the events are related or not.
