As in Example 5.5, suppose Jimmy shoots against a target with the probability of hitting the target being p, and successive shootings are assumed independent. This time he is told that a prize is awarded if he chooses to shoot 2n times and hits the target at least n times. He has been offered the choice of n. Find for which values of p he wins the prize if n = 1, 2, 3, 4, 5.

Note: For n ≥ 2, it may not be easy to solve the corresponding inequality for p, and so you can find the solution either graphically or, preferably, using the command NSolve[f[x]==0,x].