A study shows that approximately 25% of all businessmen who wear ties wear them so tightly that they reduce blood flow to the brain. At a board meeting of 15 businessmen, all of whom wear ties, what's the probability at least one tie is too tight?

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Answer 1 · 2017-02-10T15:01:52

$P("at least one too tight") = 0.9866$ (4dp)

We are told that:

$P("tight tie") = 25/100 = 1/4$
$P("not a tight tie")=1-1/4=3/4$

And so;

$P("at least one too tight") = 1 - P("none are too tight")$
$" " = 1-(3/4)^15$
$" " = 0.986636 ...$