Question

What are the answers and how do you solve them?

Answer 1

`1/512,1/8,1/64,1/32,3/32` and Independent

Explanation:

Assuming that (the area, therefore probability of landing is):
Red: 1/2
Blue: 1/4
Green:1/8
Yellow:1/4

`P(green,green,green)=1/8xx1/8xx1/8=1/512`
`P(red,red,red)=1/2xx1/2xx1/2=1/8`
`P(blue,blue,blue)=1/4xx1/4xx1/4=1/64`
`P(blue,blue,red)=1/4xx1/4xx1/2=1/32`

`P("two blues and one red")=3C1xx1/4xx1/4xx1/2`

3C1 means "ways to choose 1 out of 3". We multiply this because we need to consider all the combinations of two blues and one red we can spin. We need to find "ways 1 out of 3 can be red".
Using the combination formula:
`P("two blues and one red")=(3!)/((3-1)!1!)xx1/4xx1/4xx1/2`

`P("two blues and one red")=(3xx2xx1)/((2xx1)1)xx1/4xx1/4xx1/2=3/32`

Is this an example of an independent or dependent event?
It is independent, the previous spin does not effect the outcome of the next spin.