Archive > The Amazing Race 15 Spoilers
TAR15 EP8: "This is the Worst Thing I’ve Ever Done in My Life"
redskevin88:
--- Quote ---4 hours, 100 water logged hay bales later...
--- End quote ---
http://twitter.com/sammcmillen
Slowhatch:
This week was no exception, so I guess this blog has it right: the producers really like the accordion.
Chateau d If:
--- Quote from: apskip on November 08, 2009, 09:27:59 PM ---It's time for some statistics. The average probability of a hit with 7 flags and 186 bales is 3.76% per attempt assuming that all teams left no clues in their bales. That means that it would take an average of 26.6 tries before a team found one flag. Although it could vary as flags are actually found, on average it would still stay roughly the same unless there was a "run on the bank". Sam with over 100 tries would have taken 4 times the average. Somebody has to be above average and others below average because that the way a random task works. It is hard to say how long it took to unroll each bale and get to the next one. My guess is that it was about 2 minutes per try. That means that the average time to complete would be about 53 minutes. Meghan reported 2 hours plus. Gary had 2 hours 45 minutes for his. Sam took longer than Meghan and probably longer than Matt. Maybe 3 hours? Big Easy took a short time and so did Brian.
In comparison to the AR6 Ep. 3 Lena effort, the original specs were for 20 clues in 270 bales with 9 teams. This time there were more bales and fewer clues when the number of teams were equalized. The statistics for the original ROADBLOCK were 7.4% hit rate, almost exactly twice the percentage for AR15 ep. 8. The number of bales were 30 per team originally and 37.2 for AR15. On any measure, AR15 Ep.8 was consdeirably tougher than the original.
--- End quote ---
Actually, just multiplying 7/186 to get your odds of success only works for a very small number of trials (like one trial #1 to be exact). The more accurate determination of the odds of finding a hay bale with a flag comes from consideration that the number of remaining hay bales is getting smaller with each successive trial.
Consider the probability of not getting a flag in the 1st hay bale: 1 - 7/186 = 0.9624
Then the probability of not getting a flag in the second hay bale is: 1 - 7/185 = 0.9622
But to get to that point we have to multiply the two probabilities. So the probability that no flag will be found after two tries is: (1 - 7/186)*(1 - 7/185) = 0.9260
Then the probability of not getting a flag in the third hay bale is: 1 - 7/184 = 0.9620
But to get to that point we have to multiply the three probabilities. So the probability that no flag will be found after three tries is: (1 - 7/186)*(1 - 7/185)*(1 - 7/184) = 0.8908
And so on and so on. The probabilities of not getting a flag after the first 100 tries is:
This
many This
tries Probability
1 0.9624
2 0.926
3 0.8908
4 0.8567
5 0.8238
6 0.7919
7 0.7611
8 0.7313
9 0.7025
10 0.6747
11 0.6479
12 0.622
13 0.597
14 0.5728
15 0.5495
16 0.527
17 0.5053
18 0.4844
19 0.4642
20 0.4447
21 0.4259
22 0.4078
23 0.3904
24 0.3736
25 0.3575
26 0.342
27 0.327
28 0.3126
29 0.2988
30 0.2855
31 0.2727
32 0.2604
33 0.2486
34 0.2372
35 0.2263
36 0.2158
37 0.2057
38 0.196
39 0.1867
40 0.1778
41 0.1693
42 0.1611
43 0.1533
44 0.1458
45 0.1386
46 0.1317
47 0.1251
48 0.1188
49 0.1128
50 0.107
51 0.1015
52 0.0962
53 0.0912
54 0.0864
55 0.0818
56 0.0774
57 0.0732
58 0.0692
59 0.0654
60 0.0618
61 0.0584
62 0.0551
63 0.052
64 0.049
65 0.0462
66 0.0435
67 0.041
68 0.0386
69 0.0363
70 0.0341
71 0.032
72 0.0301
73 0.0283
74 0.0265
75 0.0248
76 0.0232
77 0.0217
78 0.0203
79 0.019
80 0.0178
81 0.0166
82 0.0155
83 0.0145
84 0.0135
85 0.0126
86 0.0117
87 0.0109
88 0.0101
89 0.0094
90 0.0087
91 0.0081
92 0.0075
93 0.0069
94 0.0064
95 0.0059
96 0.0054
97 0.005
98 0.0046
99 0.0042
100 0.0039
So you can see that the odds are better that 50% that a racer could find a flag after looking through 18 hay bales in tonight's show.
Doing the same analysis with season 6's twenty clues in 270 hay bales results in having to check only 9 hay bales.
So they had it easy back then. Though Lena may differ! :waves:
Jobby:
Nice statistics there!
walkingpneumonia:
Not sure if this was captured already - but the unused detour I believe was in Sigurdsristning:
http://www.sim1.se/swe/mal/sigurd/sigurd_01.html
Still trying to find the exact location in GE
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