The function f (x) = kxⁿ (1 - x)^m, 0 ≤ x ≤ 1 where n > 0, m > 0, and k is a constant, can be used to represent various probability distributions. If k is chosen such thatthen the probability that x will fall between a and b (0 ≤ a ≤ b ≤ 1) is

The probability that ore samples taken from a region contain between 100a% and 100b% iron is

where x represents the proportion of iron. (See figure.)

(a) What is the probability that a sample will contain between 0% and 25% iron?(b) What is the probability that a sample will contain between 50% and 100% iron?

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S₁ f(x) dx = 1