The answer to the given problem is 5
Probability is the degree to which an occurrence is likely to take place, as determined by the proportion of favorable examples to the total number of instances for which it is probable to have occurred.
Let's assume
1 - P(no one has the same sign) >= 0.5
P(two or more people have the same sign) = 1 - P(no one has the same sign)
= 1 - (12 / (12-n)) / 12^n
1-0.5=0.5 >= P (no one has the same sign) = 12/(12^n x (12-n))
0.5 >= 12 /(12^n x (12-n))
Solve for n.
n = 5
Hence the answer is 5
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