### Home > GC > Chapter 10 > Lesson 10.1.4 > Problem10-40

10-40.

The spinner at right is designed so that if you randomly spin the spinner and land in the shaded sector, you win $1{,}000{,}000$. Unfortunately, if you land in the unshaded sector, you win nothing. Assume point C is the center of the spinner.

1. If $m\angle{ACB} = 90°$, how many times would you have to spin to reasonably expect to land in the shaded sector at least once? How did you get your answer?

1. What if $m\angle{ACB} = 1°$? How many times would you have to spin to reasonably expect to land in the shaded sector at least once?

2. Suppose $P$(winning $1{,}000{,}000$) $=\frac { 1 } { 5 }$ for each spin. What must $m\angle{ACB}$ equal? Show how you got your answer.

$4$ times
$\frac{360^{\circ}}{5}=72^{\circ}$