A person clams to be able to detectwater by using a dousing rod. A dousing rod i

Question

A person clams to be able to detectwater by using a dousing rod. A dousing rod is a forked stick heldin both hands that strongly points downward over water when held bysomebody who claims to have this particular psychic ability. Inorder to test this claim, The Amazing Randy, a former magician andpsychic debunker, hosted a TV show where among other things, aperson claiming to have the psychic “dousing” abilitywas presented on-stage with 10 identical 50 gallon drums. Some ofthe drums were filled with water; the others were filled withanother liquid, containing no water. The douser was to walk pasteach drum holding the dousing rod and determine the contents ofeach drum. The douser correctly identified the contents of 7 drums.What is the probability that someone who was just guessing couldhave done as well or better than the douser?

Explanation / Answer

IF someone is randomly guessing then probability of correctlyguessing = 0.5

Then P(x >= 7) follows a binomial distribution with n = 10and p = 0.5 .

P( x = 7) = 10c7 * 0.5^10 = 11.71%

P(x = 8 ) = 10c8 * 0.5^10 = 4.39%

P(x= 9) = 10c9 *0.5^10 = 0.97%

P(x=10) =10c10*0.5^10 = 0.097%

Therefore p(x>= 7 ) = 11.71%+4.39%+0.97%+0.097% = 17.18%

Interesting thing here is that this probability doesn’tdepend on number of drums with water.

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