4) [10] Rivers at A, B, and C are shown in the figure below. Flood levels at A a

Question

4) [10] Rivers at A, B, and C are shown in the figure below. Flood levels at A and B, above mean flow level, are as follows: Flood Level at A Flood Level at B (ft Probability (ft) Probability 0.25 0.25 0.25 0.25 0.20 0.20 0.20 0.20 0.20 4 4 Assume that the flow velocities and widths at A, B, and C are the same. What is the probability that the flood a C wl be higher than 6ft above the mean level? Assume independence between flood levels at A and B. (Note that independence is assumed for the sake of simplicity and is not likely to be the case in reality.)

Explanation / Answer

Flood at C will be higher than 6 feet for the following combinations of floods at A & B: (0,8); (2,6); (2,8); (4,4); (4,6); (4,8); (6,2); (6,4); (6,6); (6,8).

So the Probability (flood at C > 6) = Probability (flood at A=0) * Probability (flood at B = 8) + Probability (flood at A=2) * Probability (flood at B = 6) + Probability (flood at A=2) * Probability (flood at B = 8) + Probability (flood at A=4) * Probability (flood at B = 4) + Probability (flood at A=4) * Probability (flood at B = 6) + Probability (flood at A=4) * Probability (flood at B = 8) + Probability (flood at A=6) * Probability (flood at B = 2) + Probability (flood at A=6) * Probability (flood at B = 4) + Probability (flood at A=6) * Probability (flood at B = 6) + Probability (flood at A=6) * Probability (flood at B = 8) = 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 + 0.25 * 0.2 = 10 * 0.25 * 0.2 = 10*0.05 =0.5

So the Probability (flood at C > 6) = 0.5

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