Chapter CSB1.13, Problem 9E

To determine

To calculate: The probability of winning a prize.

Answer to Problem 9E

  $\frac{5}{9}$

Explanation of Solution

Given information:

Following board is given:

  

Win Condition:

Coin must land on the odd numbered triangle.

Formulae used:

  $\text{P}\left(\text{specific}\text{region}\right)\text{=}\frac{\text{area of specific region}}{\text{area of the target}}$

Calculation:

The given board is divided into 9 triangles of same size. Now,

Area of complete board $=\frac{1}{2}\times 21\times 24$

  $=252$

  $\text{Area}\text{of}\text{each}\text{small}\text{triangle}\text{=}\frac{\text{Area}\text{of}\text{board}}{\text{9}}$

Thus,

  $\text{Area}\text{of}\text{each}\text{small}\text{triangle}\text{=}\frac{\text{252}}{\text{9}}=28$

Since there are 5 odd numbered triangles so area of specific region = $5\times 28=140$

Thus,

  $\begin{array}{c}\text{P}\left(\text{winning}\right)\text{=}\frac{\text{140}}{\text{252}}\\ =\frac{20}{36}\\ =\frac{5}{9}\end{array}$