Question

Consider a dart board made of three concentric circles of radii 1 cm, 2cm and 3 cm, respectively. The points you obtain by hitting different regions of the board are as follows: • 50 points if the dart lands anywhere within the circle of radius 1 cm. • 30 points if the dart lands within the circle of radius 2 cm but outside the circle of radius 1 cm. • 20 points if the dart lands outside the circle of radius 2 cm but within the circle of radius 3 cm. Suppose that in 10 independent attempts, you have never hit the outermost ring (i.e, where you score 20). Every dart hits the board somewhere. In that case, what is your expected score, given that you never miss the board? Pick ONE option 0400 Clear Selection

Answer 1

The answer to this is 350

Answer 2

The answer is 350 points

Explanation:

The Area of a circle is πr∧2

The problem states that in the attempts, you never hit the outermost ring in the 10 attempts so we need the area of the 1cm and 2cm circles

Area of the 1st circle; π X 1∧2 = π

Area of the Second circle; π X 2∧2 = 4π

We also need the area which is the difference between the area of the 1cm and 2cm circle

4π - π = π

Points 50 = π/4π = 1/4

points 30 = 3π/4π = 3/4

For one attempt,

E(x) = 50 x 1/4 + 30 x 3/4

= 12.25 + 22.5

= 34.75

This is approximately 35

Therefor, 10 individual attempts will be 10 x 35 = 350