When you take this test, you may make some correct guesses just by chance. If you have 4 tries, you may get any where from 0 to 4 correct. If you are guessing randomly, there is a probability of getting 0 correct by chance, 1 correct by chance, 2 correct by chance, and so forth. The probability of making a certain number of correct guesses by chance is an example of what is called a binomial distribution. The probability of a certain number of correct guesses by chance is found by using the following formula:

pr = (n! / (r! n-r!)) pr qn-r
where

pr = probability of r successes in n tries.
r = number of successful guesses out of n tries.
n = total number of tries.
p = the probability of a correct guess on 1 try. (In this test p = .2 or 1 out of 5)
q = the probability of an incorrect guess on 1 try. (In this test q = .8)

n! = n factorial = (1 x 2 x 3 x .... x n) or 1 if n = 0
r! = r factorial = (1 x 2 x 3 x .... x r) or 1 if r = 0
(n-r)! = n-r factorial = (1 x 2 x 3 x .... x (n-r)) or 1 if (n-r) = 0

As an example let's find the probability of getting 0, 1, 2, 3, and 4 correct guesses out of 4 tries.

p0 = (4! / (0! 4!)) .20 .84
p0 = (24 / (1 24)) 1 .4096 = 1 1 .4096 = 0.4096

p1 = (4! / (1! 3!)) .21 .83
p1 = (24 / (1 6)) .2 .512 = 4 .2 .512 = 0.4096

p2 = (4! / (2! 2!)) .22 .82
p2 = (24 / (2 2)) .04 .64 = 6 .04 .64 = 0.1536

p3 = (4! / (3! 1!)) .23 .81
p3 = (24 / (6 1)) .008 .8 = 4 .008 .8 = 0.0256

p4 = (4! / (4! 0!)) .24 .80
p4 = (24 / (24 1)) .0016 1 = 1 .0016 1 = 0.0016

As you can see, the probability of making 3 or 4 correct guesses out of 4 tries is rather low. If someone can do this well, then it is unlikely that their performance was due to chance guessing.

However, it is quite likely that a person may get 0 or 1 correct out of 4 tries even if they have no ability to foresee what the computer will generate.

So, to get in the record book your number of correct guesses must exceed the highest maximum probability category for the number of tries you make. In this example, you would have to make at least 2 correct out of 4, because the highest maximum probability category is 1 correct guess.

In addition, your probability must be lower than the current 10th place person in the record book.

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