First slide

Introduction to probability

Question

In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is

Moderate

A

$\frac{2^{n} C_{2}}{^{(^{n} C_{2} - n)} C_{2}}$
B

$\frac{{}^{n (n - 1)}C_{2}}{{}^{(^{n} C_{2} - n)}C_{2}}$
C

$\frac{^{n} C_{4}}{^{(^{n} C_{2} - n)} C_{2}}$
D

none of these

Solution

When 4 points are selected, we get one intersecting point.
So, probability is
$\frac{^{n} C_{4}}{^{(^{n} C_{2} - n)} C_{2}}$

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