Chapter 10, Problem 30RP

To determine

To find : Probability that a second - tangent angle is formed.

Answer to Problem 30RP

  $0.6$

Explanation of Solution

Given information :

Out of five segments PA, PB, PC, PD and PE are secant segments to circle O; and the remaining two are tangents to circle O.

Formula Used:

  ${}^n{c}_r=\frac{n!}{r!(n-r)!}$

Calculation :

Number of ways to select two tangent = ${}^5{c}_2$ . Cases in which secant − tangent angle will be formed = {(PE, PB), (PE, PC), (PE, PA), (PD, PA), (PD, PC), (PD, PB)}

Probability = $\frac{6}{{}^5{c}_r}=\frac{6\times 3!\times 2!}{5!}=0.6$