New Posts For Thread: Probability Quiz Question.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-questionThis is from yesterday's Guardian newspaper. The reason I am putting it up here is that I disagree with the printed answer. Tell me what you think the correct answers should be. Here it is exactly as it as it is printed."The key to the box in whichtopnag1, you are wrong because you choose to ignore the fact that this experiment would end 25 % of the times when you find the key in the first pocket you are looking.These 25 % of failed attemys has to be included in the probablities calculation.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471587573#471587573topnag1, you are wrong because you choose to ignore the fact that this experiment would end 25 % of the times when you find the key in the first pocket you are looking.These 25 % of failed attemys has to be included in the probablities calculation.Mon, 25 Oct 2010 09:45:05 -0500If in the lab coat, it is equally likely to be in the left as the right pocket. This is new information and so changes the initial probability.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471585937#471585937If in the lab coat, it is equally likely to be in the left as the right pocket. This is new information and so changes the initial probability.Mon, 25 Oct 2010 09:31:34 -0500Believe me I am trying to figure it out! OK here is another way of looking at it... Suppose that the answer printed in the paper is correct and the probability of the key being in the right pocket really is 1/3 as stated. For this to be the casehttps://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471512229#471512229Believe me I am trying to figure it out! OK here is another way of looking at it... Suppose that the answer printed in the paper is correct and the probability of the key being in the right pocket really is 1/3 as stated. For this to be the caseSun, 24 Oct 2010 17:02:30 -0500It is similar to the monty hall problem (it was probably the inspiration for this problem).Try to figure it out topnag If you don't understand the solution, you could try doing a simulation. At least that will show you what the correct answer shouldhttps://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471502353#471502353It is similar to the monty hall problem (it was probably the inspiration for this problem).Try to figure it out topnag If you don't understand the solution, you could try doing a simulation. At least that will show you what the correct answer shouldSun, 24 Oct 2010 15:51:17 -0500I have just looked up the Monty Hall problem on Wikipedia and it has not helped my certainty at all.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471501809#471501809I have just looked up the Monty Hall problem on Wikipedia and it has not helped my certainty at all.Sun, 24 Oct 2010 15:47:50 -0500Back to the original question which goes on to state "you look in the left pocket and it is empty." The question asked is this...."what is the probability of the key being in the right pocket?" So there are only two possible locations for the key.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471501169#471501169Back to the original question which goes on to state "you look in the left pocket and it is empty." The question asked is this...."what is the probability of the key being in the right pocket?" So there are only two possible locations for the key.Sun, 24 Oct 2010 15:44:10 -0500No because it states that the combined probability of the key being in either coat pocket is 0.5.Using your logic, if we expanded the possible locations to 100 (the box and a lab coat with 99 pockets), there would be a 1% of the key being in the box.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471498365#471498365No because it states that the combined probability of the key being in either coat pocket is 0.5.Using your logic, if we expanded the possible locations to 100 (the box and a lab coat with 99 pockets), there would be a 1% of the key being in the box.Sun, 24 Oct 2010 15:25:41 -0500The Investor,Let me cut straight to your last sentence. "Given that the initial probability of the key being in the lab coat is 0.5" (I am with you here) "and that it is equally likely to be in either pocket" (no problem so far), "the probability ofhttps://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471494605#471494605The Investor,Let me cut straight to your last sentence. "Given that the initial probability of the key being in the lab coat is 0.5" (I am with you here) "and that it is equally likely to be in either pocket" (no problem so far), "the probability ofSun, 24 Oct 2010 15:02:54 -0500Topnag, you say:Q1 merely stated that:C(coat) =0.5B(box)=)0.5But it states more than this, see underlined:"The key to the box in which Erwin has locked his cat, Stoppard, is either in his lab coat (probability 1/2) or in the box with the (probabilityhttps://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471488209#471488209Topnag, you say:Q1 merely stated that:C(coat) =0.5B(box)=)0.5But it states more than this, see underlined:"The key to the box in which Erwin has locked his cat, Stoppard, is either in his lab coat (probability 1/2) or in the box with the (probabilitySun, 24 Oct 2010 14:29:29 -0500Ach, should read "subtract C2 and you are left with C1=B". But you got my meaning.https://community.betfair.com/general_betting/go/thread/view/94082/26121785/probability-quiz-question?post_id=471482505#471482505Ach, should read "subtract C2 and you are left with C1=B". But you got my meaning.Sun, 24 Oct 2010 13:54:02 -0500