Independently of each other, ten numbers are randomly drawn from the interval (0, 1). You may view the numbers one by one in the order in which they are drawn. After viewing each individual number, you are given the opportunity to take it or let it pass. You are not allowed to go back to numbers you have passed by. Your task is to pick out the highest number. Your strategy is as follows. If, after you have viewed a number, there are still k numbers left to view, you will take the number if it is the highest number to appear up to that point and if it is higher than a critical level a_k, where a₀ = 0, a₁ = 0.500, a₂ = 0.690, a₃ = 0.776, a₄ = 0.825, a₅ = 0.856, a₆ = 0.878, a₇ = 0.894, a₈ = 0.906, and a₉ = 0.916. Use simulation to determine the probability that you will pick out the highest number.