Pdoggg Posted July 8, 2015 Share Posted July 8, 2015 R67 and I were debating this question for hours last night via PM with neither of us budging on our answer. Any other opinions? Quote Link to comment
Tomcat Posted July 13, 2015 Share Posted July 13, 2015 R67 and I were debating this question for hours last night via PM with neither of us budging on our answer. Any other opinions? 25% of the time is HH without knowing that at least one would land heads but im not sure if that matters here as we have to assume that both coins are tossed at same time ! The 4 states possible are ( if you tossed the coins into two cups say side by side HH HT TH TT this is if two coins are tossed and then seen as one result. However it could be a twist on the Monty Hall Problem where one piece of the information is known or given away.... maybe the question could have been clearer if this is the case ot maybe i need to think about it again Quote Link to comment
Kahuna Posted July 13, 2015 Share Posted July 13, 2015 25% of the time is HH without knowing that at least one would land heads but im not sure if that matters here as we have to assume that both coins are tossed at same time ! I vote for TC's answer.............. I think his answer is spot on........... Hope I didn't doom you TC.......... I flunked both parametric and non-parametric statistics courses....... At least I was consistent........ Quote Link to comment
Tomcat Posted July 14, 2015 Share Posted July 14, 2015 ya..ha ha Two coins have been tossed and hidden under two cups. Under one cup i can show you that its a head ,, what is the chance now of the other coin being a head and then its still 25% ovrall probability for the total outcome still being HH , or maybe the way the question is phrased means im wrong ... its all good fun...i think this is the case in fact as part of the info has been revealed .. ooops Therefore i may be wrong Quote Link to comment
Kahuna Posted July 15, 2015 Share Posted July 15, 2015 I didn't read the original question and didn't realize that one of the coins landed heads...Remember I flunked... Maybe not reading was one of the reasons.............. Knowing that would automatically dismiss TT as an option.....I am indeed a moron.......... However, I do think it matters which coin landed heads.............. If the second coin landed heads then that opens the feasibility of three possibilities...HH, TH, HT.... In that scenario TH and HT are not the same....Therefore it clearly does depend on how we interpret the question.... So I say 33% probability the other coin - either first or second flipped coin - will be a head......... I think I flunked again.................. Except.............. From a ladyboy forum perspective the answer should always be HT - head and then tail............ But perhaps on occasion TH - tail and then head........ Either way it always depends on how much coin is in your pocket.............. Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 The wording of the coin question is what is catching people out. 'At least one of them lands heads' is the same as saying we only need to flip ONE coin, as we know the end state for one of the coins. Which one? For the question that was asked, it does not matter. How many possible end states for the remaining coin? Only 2, H or T. Thus, we have a probability of 1 in 2. I have a feeling that people are answering the question they think was asked rather than the question that was actually asked. Quote Link to comment
Pdoggg Posted July 15, 2015 Share Posted July 15, 2015 'At least one of them lands heads' is the same as saying that the outcome is either HT, TH, or HH. We are told that TT did not happen. So I see it as 3 equally probable possibilities so a 1 in 3 chance that both coins are heads. R67 and I went around and around on this for hours with neither of us changing our mind. Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 I have a feeling that people are answering the question they think was asked rather than the question that was actually asked. You have just amply demonstrated my point, pdoggg! Quote Link to comment
Tomcat Posted July 15, 2015 Share Posted July 15, 2015 PD is right according to the maths guys i do believe... Quote Link to comment
Tomcat Posted July 15, 2015 Share Posted July 15, 2015 OK the Monty Hall question Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 Even the guy who originally set the question that was asked later admitted that he got it wrong. And I don't mean Lefty. Pdoggg has a link to the mathematical paper in which he admits the setting of the question is wrong. Pdoggg and others are answering a question correctly, but not the question that was asked. Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 In fact, let me break this down to its simplest form. What does the question actually ask? I flip two coins. At least one of them lands heads. What is the probability that both land heads? OK - let's make it even more simple: Two coins. One of them is heads. What is the probability that both are heads? Answer: 1 in 2. End of. Draw a line under it. The fat lady has sung. Elvis has left the building. Stick a fork in this one. Coz it. Is. Done. Quote Link to comment
Pdoggg Posted July 15, 2015 Share Posted July 15, 2015 OK the Monty Hall question Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Yes. It is to my advantage to switch doors. 1 Quote Link to comment
Tomcat Posted July 15, 2015 Share Posted July 15, 2015 correct PD .. this caused a big stir when it come out and cought out even professors Quote Link to comment
Tomcat Posted July 15, 2015 Share Posted July 15, 2015 In fact, let me break this down to its simplest form. What does the question actually ask? I flip two coins. At least one of them lands heads. What is the probability that both land heads? OK - let's make it even more simple: Two coins. One of them is heads. What is the probability that both are heads? Answer: 1 in 2. End of. Draw a line under it. The fat lady has sung. Elvis has left the building. Stick a fork in this one. Coz it. Is. Done. its 1 in three Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 No. It is not. Quote Link to comment
Tomcat Posted July 15, 2015 Share Posted July 15, 2015 if two coins then its HH option 1 HT option 2 TH option 3 since there are TWO coins you dont know if the given head is the left or right one so must be three options.. thats what some maths bod has stated ...ill dig it out later .. Quote Link to comment
Whateva Posted July 15, 2015 Share Posted July 15, 2015 if two coins then its HH option 1 HT option 2 TH option 3 since there are TWO coins you dont know if the given head is the left or right one so must be three options.. thats what some maths bod has stated ...ill dig it out later .. So you are say a head and a tail is different to a tail and a head ... Diii dooooohhhh ... Not where i come from Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 Thank you, Whateva. Finally, someone who sees sense. Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 if two coins then its HH option 1 HT option 2 TH option 3 since there are TWO coins you dont know if the given head is the left or right one so must be three options.. thats what some maths bod has stated ...ill dig it out later .. ...and he is wrong as well. Read the question again. Left and Right? That is entirely inconsequential to the question being asked! Let's designate our coins a posteriori, rather than a priori, H and X. Why can we do this? Because the question clearly states that 'at least one of them lands heads.' I know that's not what happens in reality, but we are not dealing with reality, we are dealing with a Lefty-posed question. For the avoidance of any doubt, this question is stating that one of the coins will always land heads, but does not state which. Why? Because that is not important in the question that was asked. The one that lands heads - and, remember, the question that was asked clearly states that 'at least one of them lands heads' - we can designate H. The other coin, X, can have how many states? Answer - only 2, T and H. Thus, for the question that was asked, the probability that both coins land heads (HH) is 1 in 2. It does not matter one jot in this question asked by Lefty whether we flip the coins one by one or simultaneously. If we do it one by one: We flip the first coin, and it lands H. The second coin can land H or T. Thus we have 2 possible end states for the question that was asked. Probability = 1 in 2. or We flip the first coin, and it lands T. We don't even need to flip the second coin now as we can assume that it will land H (in order to fulfill the conditions of the question that was asked). So in this scenario, it's the first coin that can have 2 possible states, as the second coin can be said to have a known end state, H. Again, probability for coin 1 = 1 in 2. To put it more simply, for the question asked, the two scenarios for one-by-one are identical, and thus one of them is redundant. Now let's flip simultaneously. We already know, from the question asked, that 'at least one of them lands heads,' and so we only need to focus on the remaining coin, X. It can only have 2 possible end states, thus giving us a probability of 1 in 2. Is my highlighting not working on anyone else's computer/phone? Is there some kind of word blindness epidemic sweeping the forum? What is it about the wording of the question that is so difficult for you all to understand? If you break the question down, you are dealing with ONLY ONE COIN BEING TOSSED. Thus, your probability is 1 in 2. Quote Link to comment
Kahuna Posted July 15, 2015 Share Posted July 15, 2015 "If the original question was: "You flip two coins. The first one came up heads. What are the chances that the second one is also heads?"Then you would be correct to say 50%. But since the question was: "You flip two coins. ONE OF THEM came up heads. What are the chances the second one is also heads?"Then the answer is 33%." Quote Link to comment
Guest LaBambaBar Posted July 15, 2015 Share Posted July 15, 2015 No, Kahuna. You must read the question again. Quote Link to comment
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