A frog moves home to a narrow strip of pond along which there are 5 evenly spaced lily pads. From each lily pad, the frog has an equal chance of jumping to the pad on either side until it reaches the pad at either end. Here the frog will sit indefinitely to feed off the abundant supply of flies now accessible to it.

a. If the frog begins on the middle lily pad, calculate the probability that it has not eaten within 3 jumps.

b. Estimate the probability that a frog beginning on a random lily pad will never eat.