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Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)



On 2/18/2014 9:46 AM, Rauber, Joel wrote:
The second list was the random list. As noted, one cannot prove which one was the random list, you can only make a probabilistic guess.
/snip/the Math Prof. told me that the probability of consecutive numbers appearing on a truly random list is 48%, much higher than most people would guess.


I attempted to confirm the expectation of at least two consecutive numbers
in a 21,5 set, like this:

There are 34 couplets of two consecutive numbers in the range 1..35
The combinations of any 2 numbers in 35 are 595
It follows that the chance of at least one consecutive couplet in
a row is 34 in 595 and the chance of no consecutive couplet in
a row is 561 in 595.
It follows that the chance of no consecutive couplet in 21 rows is
0.29, and the chance of at least one consecutive couplet in a
21 row set is 71%

Unfortunately, this does not agree with Joel's input which was 48%,
so I expect that I slipped. But where?


Brian Whatcott Altus OK