In order to drill a well, the water depth needs to be known. In preliminary designs, water depth is divided into four categories: less than 5 m, between 5 and 10 m, between 10 and 15 m, and more than 15 m. The following assumptions are known based on the experiences of the hydrology of the area:

The probability of depth to be less than 5 m = Pr [B1] = 0.6.

The probability of depth to be between 5 and 10 m = Pr[ B2] = 0.2.

The probability of depth to be between 10 and 15 m = Pr [B3] = 0.15.

The probability of depth to be more than 15 m = Pr [B4] = 0.05.

The depth h is measured and tabulated in Table 10.2 (the depth includes measurement error).

The h value is obtained at 7 m from the measurements. Considering the error measurements and other assumptions, calculate the probability of h to be in each category.

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TABLE 10.2 Probability of Correctness of Measurements h5 5