Question

Use the dartboard below to calculate the expected values in terms of r1=2 bull`s eye worth 3 points r2=4 middle ring worth 1 point r3=2 square root 6 outer ring worth -1 point
A) 2/3 points B) 1/6 points C) 16 points D)4/11 points

Answer 1

Expected value: \[ \Large
E[X] = \sum_x xp(x)
\]Where \(x\) would be the number of points and \(p( x)\) is the probability of getting \(x\) points.

Answer 2

what!

Answer 3

Okay, so you get every possible outcome... you multiply the points you'd get for that outcome by the probability it happens.... then you add all of this up.

Answer 4

"Use the dartboard below"

??

Answer 5

Is r1, r2, r3, etc the radius?

Answer 6

yeah

Answer 7

Okay, so what we'll do is calculate the area of each ring. We'll assume that you must hit the dart board and that every point has an equiprobable chance of being hit.

Answer 8

Then p(x) = Area of x / Total Area

Answer 9

@Brittanyy! Get it yet?

Answer 10

kind of im gonna guess it is a

Answer 11

Don't guess, try

Answer 12

What is the area of the bulls eye area?

Answer 13

I would if I understood how you want me to set this problem up to solve it but I have no idea

Answer 14

Start just by calculating the area of each scoring region. Can you do that?

Answer 15

so the area for r1 would be 2/3?

Answer 16

for the bulls eye. I'm getting \(\pi2^2\)

Answer 17

for the middle ring, I'm getting \(\pi4^2-\pi2^2\)

Answer 18

and for the outer ring I get \(\pi 2^2 6 - \pi 4^2\)
lastly my total area is \(\pi 2^2 6\)

Answer 19

how are you getting that though?

Answer 20

Well I'm subtracting the inner circle from the outer circle to get the area of the ring.

Answer 21

The area of a circle is \(\pi r^2\)

Answer 22

okay then what do I do?

Answer 23

So divide the area of each region by the total area of the dart board.