Two small rivers A and B meet and become a larger river C. For a new housing pro

Question

Two small rivers A and B meet and become a larger river C. For a new housing project, the flood level, defined as the water level above the mean level of river C, is under considera¬ tion. Past records indicate that a 1-ft change in the water level of river A causes a 0.5-ft change in the water level of river C, and a 1-ft change in the water level of river B causes a 0.25-ft change in the water level of river C. The flood levels of rivers A and B can be esti¬ mated precisely. However, they are equally likely to be 0, 1, 2, and 3 ft for both rivers. Assuming statistical independence of flood levels between rivers A and B, what is the prob¬ ability that the flood level of river C will exceed 2 ft?

Explanation / Answer

P(that the flood level of river C will exceed 2ft) = Only one possible case, when the flood levels in A and B are both 3 ft

since change in river level of C will be = 3 * 0.5 + 3 * 0.25 = 2.25

For change of 3 in A and 2 in B, it will be change of 3 * 0.5 + 2 * 0.25 = 2, which doesn't exceed 2

Since it is equally probable, that flood level of (0ft = 1ft = 2ft = 3ft) = 0.25

Probability of the event = P(3 ft rise in A) * P( 3 ft rise in B)

=> 0.25 * 0.25

=> 0.0625

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