The analysis of results from a leaf transmutation experiment (turning a leaf int

Question

The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed: A naturalist randomly selects three leaves from this set, without replacement. Determine the following probabilities. (a) Exactly one has undergone both types of transformations. (b) At least one has undergone both transformations. (c) Exactly one has undergone one but not both transformations. (d) At least one has undergone at least one transformation. Round your answers to four decimal places (e.g. 98.7654). (a) The probability is (b) The probability is (c) The probability is (d) The probability is

Explanation / Answer

a) Let X be the number of people undergone both transformations
P(X = 1) = [245C1 * 55C2]/300C3 = 0.08166

b) P(X >= 1) = 1 - P(X = 0)
P(X = 0) = [245C0 * 55C3]/300C3 ,
P(X >= 1) = 1 -  [245C0 * 55C3]/300C3 = 0.9941

c) Let x be the number of people undergone only one transformation.
P(X = 1) = [37C1 * 263C2]/300C3 = 0.2861

d) P(X >= 1) = 1 - P(X = 0)
P(X = 0) = [37C0 * 263C3]/300C3
P(X >= 1) = 1 - [37C0 * 263C3]/300C3 = 0.3272

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