Thanks for the standings, NCDave. Good job!
I just re-watched the episode, and wondered about two things:
1) Did the second ferry back from the island drop the teams off at a different part of the dock? All three teams on that ferry had a more difficult time finding the clue box, whereas the teams on the first & third ferries seemed to have no trouble at all. In fact, from the way they were all grouped around the clue box, it looked like they all arrived at it at about the same time.
2) How did Alison & Donny get to do the zip plunge before Linda & Karen? The Bowling Moms completed the zip pull first (albeit by only a couple feet), yet went second on the plunge.
NCDave -- Props!!! for a most impressive analysis.
(I presume you otherwise have a life-- LOL)
It looked like Alison passed Linda to finish the first zip line task first, so they got to do the 2nd zip first.
Originally Posted by LAGuy
But I also saw how Linda was a little nervous and had Karen go first on the first zip. It occurred to me that Linda and Karen knew they were in first place and thought they'd like to see someone else go down first. If I was going to drop down a zip line into a pool that far, I'd certainly prefer to see someone else do it first to see how they did it and make sure they survived.
Thanks for the complements. I've always been interested in how teams get eliminated. It usually comes down to one or two things--sometimes mistakes and sometimes luck. Little things can have a great effect on the standings.
And I do have a life. Notice that it took me four days to get around to posting that.
I'm so far behind reading TAR stuff here that I had to go clear back to ep1 and try to catch up a little bit. And, WOW, I loves me some math and statistics, so all of the talk about the roulette was just great.
Regarding the example that was given more than once about coin-flipping. If a coin gets heads 49 times in a row, what is the probability of heads on the next flip? I get the mathematical idea trying to be presented with this example/question, but I couldn't help thinking I'd put a lot of money on heads coming up again on the 50th coin flip. Cause I'd say that is NOT a fairly balanced coin. :)
As I think someone else already posted, the correct probability of any ONE team successfully completing the roulette Detour is 43.125%, assuming the wheel had both a "0" and a "00".
Someone stated that you could estimate the probability of success on the roulette Detour as follows.
(1) the probability of success in one spin of the wheel with 5 numbers picked was about 13%
(2) the teams had 4 such spins, since they had 20 total chips
(3) so, you could just add 13% together 4 times (= 52%) to estimate the total of about 50%.
WRONG! I know that was only an estimate, but it was a very poor estimate. And, if I remember this came from a math major (shame on you :) ). Maybe you were just trying to simplify, but since the exact calculations aren't that difficult to follow, I'm not sure simplifying at such a great expense of accuracy is a good thing.
So, if they instead had 40 chips (so 8 spins of the wheel instead of only 4), you'd estimate 13% x 8 tries = roughly 100% chance for success. When in fact it would only be 67.65%. So, the "adding the probability of success on any one spin of the roulette wheel together" only becomes worse with more spins.
As far as all 4 teams successfully completing roulette. Before they started, if we knew 4 teams would try roulette, we'd have the following.
Probability(0 of 4 are successful) = 10.464%
Pr(1 of 4 is successful) = 31.736%
P(2 of 4) = 36.095%
P(3 of 4) = 18.246%
P(4 of 4) = 3.459%
Since we got 4 of 4 being successful, this was very unexpected. We should've expected either 1 or 2 to be successful.
But, it's not really *THAT* unbelievable that it happened. It was just a run of good luck.
To put it into perspective, try this. Flip a coin five times. Record the result of each flip. Repeat this experiment (ie 5 more flips) until you get a result of 5 heads. The probability of this occuring is 3.125%, almost identical to the probability that the roulette Detour would produce 4 successful teams. On average it should take you about 32 times before you hit 5 heads out of 5 flips. Some people will hit 5-for-5 right away within the first few tries. Other people will go 50 or more tries before they hit it 5-for-5. Or more likely they will give up because they are tired of flipping coins. :)
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