# 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?

Feb 10, 2017

$P \left(\text{at least one too tight}\right) = 0.9866$ (4dp)

#### Explanation:

We are told that:

$P \left(\text{tight tie}\right) = \frac{25}{100} = \frac{1}{4}$
$P \left(\text{not a tight tie}\right) = 1 - \frac{1}{4} = \frac{3}{4}$

And so;

$P \left(\text{at least one too tight") = 1 - P("none are too tight}\right)$
$\text{ } = 1 - {\left(\frac{3}{4}\right)}^{15}$
$\text{ } = 0.986636 \ldots$
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