1. ## Probabilities Logical Problem

Hi, i would like to leave you here a logical problem related with probabilities, if you can help me i would appreciate a lot!.

The problem:

You have a box with 6 glasses (A,B,C,D,E,F), and you are asked to try to pick, lets say the glass B, and you have 3 chances of picking the right glass(you can pick a glass 3 times), without returning the glasses to the Box (that are the rules, and are stated before anything).

My question is: Does make any diference, i mean probabilistically, if i just pick 3 glasses from the box or if i pick the glasses 1 by 1, i mean picking one, and if i loose, i pick another, then another???

Thats my question, from my point of view i would say its make no difference, since its stated from the beginning that you are able to pick a glass 3 times.

Would be different if i am able to pick only 1 glass, fail to pick the right glass, and THEN it is offered to me another chance to pick a glass, right??

PD: Sry for my poor english, its not my lative languaje

2. ## Re: Probabilities Logical Problem

Well if you pick three glasses out of the 6, each one worth 1/6 probability, you'd have a 50% chance (3/6) of glass B being there (being they are randomly shuffled.)
And if you pick them 1 by 1, you'd have a 1/6 probability at first, then a 1/5, and then a 1/4, which is a 37/60 probability (61.6%.)
So if my math and logic are not wrong, it is better to pick them up 1 by 1!

3. ## Re: Probabilities Logical Problem

Originally Posted by aNxello
So if my math and logic are not wrong, it is better to pick them up 1 by 1!
Do you know the five-second rule? It states that "food dropped on the ground will not be contaminated with bacteria if it is picked up within five seconds of being dropped" (Wikipedia). Few people know, but the rule applies to probability theory as well. Namely, if you pick objects with an interval less than five seconds, then the glasses are considered to be picked all together; otherwise, they are picked one by one. The probabilities will be corresponding.

Just kidding. Of course the probabilities are the same. As post #2 says, if you pick them all together, then the probability that the right glass is picked is 3/6 = 1/2. If you pick them one by one, then the probability that the right glass is picked is 1/6 + (5/6)(1/5 + (4/5)(1/4)) = 1/6 + 1/6 + 1/6 = 1/2. The second term is the probability that the right glass is not picked at first (5/6) times the probability that it is picked later, which is similarly a sum of the probability that it is picked second and the probability that it is picked last.

4. ## Re: Probabilities Logical Problem

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