Probability.

So been having a debate on skype about probability.

Here is the first scenario:

Person A rolls a die and only gets one throw. His likeliness to get a 6 is 1/6.

Person B rolls a die but gets 1 million throws does his likeliness to get a 6 increase or does it still stay 1/6 ?

Scenario B:

There is 4 bosses in a house. When you enter the building a random boss becomes active and you can fight it but this was not the boss you needed to get a certain item. You can only enter this place once a day and each time you fight 1 random boss out of the 4.

So on the first day your probability to get the boss you want is 1/4.

If you were to go in the next day would your probability to get the boss you need increase or stay the same?

Scenario A

The probability of rolling a six on a 1-6 die remains 1/6 no matter how many times it is rolled.

Scenario B.

Does each boss remain after you fight? If no, then the probability changes to 1/3 Increase, as you mentioned. If the bosses remain after the fight, then the probability remains 1/4.