On the basis of isopluvial maps the 75 year-24 hour maximum rainfall at Bangalore is found to be 25.0 cm. Determine the probability of a 24 h rainfall of magnitude 25.0 cm occurring at Bangalore: a) Once in ten successive years b) Twice in ten successive years. c) At least once in ten successive years?

Question

Answer

Probability of 24 h rainfall of magnitude 25.0 cm occurring at Bangalore

a) Once in ten successive years

To determine the probability of a 24 h rainfall of magnitude 25.0 cm occurring once in ten successive years, we need to consider the historical data and the isopluvial map for Bangalore.

From the given information, we know that the 75-year-24 hour maximum rainfall at Bangalore is 25.0 cm. This means that the maximum rainfall of this magnitude occurs once in every 75 years on average.

Therefore, the probability of a 24 h rainfall of magnitude 25.0 cm occurring in a single year can be calculated as:

P(occurrence in a single year) = 1 / 75 = 0.0133

Since we are considering ten successive years, the probability of this event occurring once in ten years can be calculated as:

P(occurrence once in ten years) = P(occurrence in a single year) * P(not occurring in the remaining nine years)

Assuming that the probability of not occurring in a single year is given by 1 - P(occurrence in a single year), the probability of not occurring in the remaining nine years is:

P(not occurring in the remaining nine years) = (1 - P(occurrence in a single year))^9

Substituting the given values, we can calculate the probability:

P(occurrence once in ten years) = 0.0133 * (1 - 0.0133)^9 ≈ 0.0133 * 0.8907 ≈ 0.0118

b) Twice in ten successive years

To determine the probability of a 24 h rainfall of magnitude 25.0 cm occurring twice in ten successive years, we can use a similar approach as in part (a).

The probability of occurrence in a single year remains the same as 0.0133.

Since we are considering ten successive years, the probability of this event occurring twice in ten years can be calculated as:

P(occurrence twice in ten years) = P(occurrence in a single year)^2 * P(not occurring in the remaining eight years)

Assuming that the probability of not occurring in a single year is given by 1 - P(occurrence in a single year), the probability of not occurring in the remaining eight years is:

P(not occurring in the remaining eight years) = (1 - P(occurrence in a single year))^8

Substituting the given values, we can calculate the probability:

P(occurrence twice in ten years) ≈ 0.0133^2 * (1 - 0.0133)^8 ≈ 0.0002

c) At least once in ten successive years

To determine the probability of a 24 h rainfall of magnitude 25.0 cm occurring at least once in ten successive years, we need to consider the complement of the event 'not occurring in any of the

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