Question 30759
Assuming all the spinners are unbiased and the same and that P(red)=P(blue)=P(orange), then we have:


P(rad) = P(blue) = P(orange) = 1/3


On first spin of the 4 tops:

P(all red) = (1/3) * (1/3) * (1/3) * (1/3)
P(all red) = (1/81)


Similarly, P(all blue) = (1/81) and P(all orange) = (1/81)


So, P(all 4 tops are the same colour) = (1/81) + (1/81) + (1/81)
P(all 4 tops are the same colour) = (3/81)
P(all 4 tops are the same colour) = 1/27


Now, spinning the top a second time produces the same result... the 2 situations are independent, since they do not affect each other.


So, P(4 same colour AND then 4 same colour again) = (1/27) * (1/27)
--> 1/729


jon.