When blindfolded, what are the odds against picking green out of 3 balls red, yellow and green.?

Question

If the first choice is not green, that ball is put back into the container and another choice is made. The container is rotating so each choice is completely random.

How do the odds against picking green increase from the 1st attempt to the 21st attempt consecutively.

Answer 1

odds 1/3

Answer 2

Why expect people to know that?You can try it out your ownself!

Answer 3

You have a 1 in 3 chance which is 33.3333333%

Answer 4

well if you are only considering the odds of not picking green, they are 2/3 for the first attempt, and each further attempt is multiplied by 2/3. So given that green wasn't picked the first time, the odds it wont be picked the second time are 4/9 (44% chance), and 8/27 (30% chance) for the third time etc. However if at any point in the 21 trials you pick green, the odds go back to 2/3 as the increase is dependant only on not picking green. If you get all the way to 21 trials, the odds that green will never have been picked are (2^21)/(3^21)

= (2097152)/(10460353203)

= 0.02% chance

then again, if you are blindfolded you wont know what you pick anyway

Answer 5

Apparently no one else thought carefully enough about your question.  For the first attempt, it is indeed 2/3.  For the rest, it isn't, because it's not an independent probability.  There are only 8 choices for the second pick.  If the first pick was not green, there are 6 choices, 4 of which are not green.  But if the first pick was green, there are only 2 choices (red,yellow), since the green ball is not returned to the container.  Now, 6 of the 8 choices (equally likely) are not green, or 3/4.  Carefully continue this reasoning to get your answer.