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Home > GC > Chapter 10 > Lesson 10.1.4 > Problem 10-40

10-40.

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

  1. If , 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?

Circle, with center, C, and points, a, and, b, on the circle, with line segments from, c, to a, and from c, to, b, creating a sector, which is shaded between points, a, and b.

  1. What if ? How many times would you have to spin to reasonably expect to land in the shaded sector at least once?

  2. Suppose (winning ) for each spin. What must equal? Show how you got your answer.

What fraction of the circle is the shaded region? How can this help you?

times

Use the same method you used for part (a).

If this is the reverse of the method used for part (a), what must you do?