Answer

Challenge Problem 2 Solution

In order for no cats to collide, all four cats must walk in the same direction. Thus, all four cats must walk clockwise OR all four cats must walk counterclockwise. This means $P(nocatscollide)=P(allcatsgoclockwise)+P(allcatsgocounterclockwise)$.

The probability a cat chooses clockwise or counterclockwise is $1/2$. So the probability all four cats choose clockwise or counterclockwise is $(1/2)*(1/2)*(1/2)*(1/2)$.

Therefore, $P(nocatscollide)=(1/2)*(1/2)*(1/2)*(1/2)+(1/2)*(1/2)*(1/2)*(1/2)=1/16+1/16=1/8.$