Chapter 13.3, Problem 19PPS

To determine

To calculate:

The probability that pointer landing on neither red nor yellow using the spinner:

Answer to Problem 19PPS

The probability that pointer landing on neither a red nor yellow using the spinner is $62.2\%$ .

Explanation of Solution

Given information:

  

Calculation:

The spinner consists of the circle with $5$ colored segments. The dark red segment is described by $30$ degree angle, the yellow segment is described by $44$ degree angle, the red segment is described by $92$ degree angle, the blue segment is described by $84$ degree angle and the green segment is described as $110$ degree angle.

Radius: $r$ : The radius of the spinner

The probability that the pointer of spinner landing on red segment is equal to the area of the red segment is:

Area of all other segment: $\frac{\left({30}^{\circ }+{84}^{\circ }+{110}^{\circ }\right)}{{360}^{\circ }}\pi r^2$

The total area of circle: $\pi r^2$

P (Pointer landing on neither a red nor yellow):

  $\begin{array}{l}P=\frac{\frac{\left({30}^{\circ }+{84}^{\circ }+{110}^{\circ }\right)}{{360}^{\circ }}\pi r^2}{\pi r^2}\\ P=\frac{{224}^{\circ }}{{360}^{\circ }}\\ P=0.622\\ P=62.2\%\end{array}$

The probability that pointer landing on neither a red nor yellow using the spinner is $62.2\%$ .