Question about adding percentages.?

Question

If I have 50% chance that I guess something and have 2 attempts to do so.

Restarting the odds after the first attempt(not adding up or taking what is left)what is my chance of guessing it just once?

And what happens when you increase the amount of attempts?

My problem is that it can't become 100% so what percentage is it?

Answer 1

What do you mean by "restarting the odds after the first attempt?"

Your odds would depend on the nature of what you are trying to guess.  If each guess attempt is totally independent of previous guesses (such as flipping a coin or rolling dice) your odds of guessing right would be exactly the same on each guess attempt.  If each guess attempts changes the nature of what you are attempting to guess (such as guess the number of 10s left in a deck of cards after seeing a card) your odds would be different at the start of each guess attempt.

Now if you are flipping coins each guess attempt would have the exact same odds (50%) on each flip.   If you are rolling a single die you would also have the same odds on each guess attempt (in this case 1/6.)

If you are guess the odds of picking a particular card out of deck of cards and discarding cards on every attempt, your first guess would have odds of 1/52.  Your next guess would have odds of  1/51 and your next guess would have odds of 1/50 and so on (this is assuming you did not already find the card you are looking for on the previous guesses.)

You have to be more specific with your question.  What is the nature of the thing you are trying to guess (coin flips, roll of a die?)  When you make a guess and guess right (or wrong) does this change the number of possible guesses on the next round?

Answer 2

Look at it this way using a coin flip as an example:  using just one coin flip, heads is 1/2 and tails is 1/2.  When you go to two coin flips you have hh, ht, th, and tt as your possible outcomes.  Adding them up, hh is 1/4, tt is 1/4 and ht or th (we consider those identical outomes) is 2/4.  And so on as you increase the number of coin flips.  This way, the probabilities always add up to 1.0.