suppose that you roll a pair of dice 1,000 times and get seven 350 times. Based on these results, what is the probabilty that the next roll results in seven?
Your dice must be weighted. But based on the results to you get the following:
The question is trying to demonstrate that, because each trial (dice roll) is independent, the probability remains the same no matter what the results from the previous dice rolls were. Therefore, your answer will just be the probability of rolling a seven, which is 1/6.
This knowledge could be important, for example, in a casino. You could be playing craps and have lost 49 times, without one win. You might assume that, because you have lost so many times, you are due for a win and you bet a lot of money on the one roll.
However, the probability of winning or losing remains the same no matter how many times you’ve won or lost, therefore you probably shouldn’t assume you’d win the next roll, or perhaps never gamble in the first place