If 3 ants are on three different vertices of a triangle. what is the probability they will collide and they can move along the sides of the triangle - so in this case each ant can move along 2 sides of the triangle. So why is the probability that they will move in a clockwise direction (1/2)^3 ?? and probability in the counter clockwise direction is (1/2)^3 again. I understand that probability of moving itself is (1/2) but why is it cubed ?
Why is this probability being cubed ?
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2Because each ant moves independently with a probability $\frac{1}{2}$ to move anticlockwise or clockwise: $$\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\left(\frac{1}{2}\right)^{3}$$ – 2012-10-08
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0so what formula is this using to get this cubed result and why is it not addition of the probabilities ? – 2012-10-08
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0@Shaktal Sorry but, for independent events, P(A or B or C)=P(A)+P(B)+P(C) is as wrong as can be. – 2012-10-08
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0just imagine it as follows: there are 8 different ways the ants can move. 000,001,010,011,100,101,110,111 where 0 is anticlockwise and 1 clockwise. $2^3=8$ – 2012-10-08