What are the answers and how do you solve them?

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1 Answer
May 15, 2018

1/512,1/8,1/64,1/32,3/321512,18,164,132,332 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=1/512P(green,green,green)=18×18×18=1512
P(red,red,red)=1/2xx1/2xx1/2=1/8P(red,red,red)=12×12×12=18
P(blue,blue,blue)=1/4xx1/4xx1/4=1/64P(blue,blue,blue)=14×14×14=164
P(blue,blue,red)=1/4xx1/4xx1/2=1/32P(blue,blue,red)=14×14×12=132

P("two blues and one red")=3C1xx1/4xx1/4xx1/2P(two blues and one red)=3C1×14×14×12

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!)xx1/4xx1/4xx1/2P(two blues and one red)=3!(31)!1!×14×14×12

P("two blues and one red")=(3xx2xx1)/((2xx1)1)xx1/4xx1/4xx1/2=3/32P(two blues and one red)=3×2×1(2×1)1×14×14×12=332

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.