Question

1. A spinner is divided into six equally sized regions. Three of the regions are labeled 4, one region is labeled 3, one region is labeled 1, and the last region is labeled 5. The spinner is spun 720 times.

(a) How many times is the spinner expected to land on 4? Show all work.
(b) How many times is the spinner expected to land on a prime number? Show all work.

Answer:

Answer 1

(a) 360

(b) 240

Explanation:

You want the expected number of times a 6-region spinner labeled 1, 3, 4, 4, 4, 5 is expect to land on (a) 4, or (b) a prime number when it is spun 720 times.

A. E(4)

Three of the six regions are labeled 4, so we expect the fraction of spins landing on 4 to be 3/6 = 1/2.

Of 720 spins, the expected number landing on 4 is 1/2(720) = 360.

The spinner is expected to land on 4 360 times.

B. E(prime)

Two of the six regions are labeled with prime numbers (3 and 5), so we expect the fraction of spins landing on a prime to be 2/6 = 1/3.

Of 720 spins, the expected number landing on a prime is 1/3(720) = 240.

The spinner is expected to land on a prime 240 times.

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