You own a very special goat. Your goat knows (with reasonable accuracy) if she is standing on a prime number and will let you know by bleating. She is still a little confused by prime numbers, though, and will bleat only 75% of the time she is standing on an actual prime number and will bleat 25% of the time when the number is not actually prime.
To test your goat, you have created a straight line of squares numbered 1 to 300 in consecutive order. You let the goat wander to a random start point on the line. Then, the goat will randomly (with equal probability) move one square to the left or right. She will look at the number she is now on and then decide to bleat or not bleat based on that number. This process continues a total of 15 times. If the goat is standing on "1" she can only move to "2" as her next move and if she is on "300" she must move to "299" as her next move.
What is the probability that during a 15-move sequence, you will hear her bleat on at least four moves in a row but no more than nine moves in a row? Show (graphically) that your solution has converged.