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What is the probability that at least 10 specimens of the

Suppose a geologist has collected 15 specimens of a certain rock, call it R1, and 10 specimens of...

Suppose a geologist has collected 15 specimens of a certain rock, call it R1, and 10 specimens of another rock, call it R2. A laboratory assistant selects randomly 15 specimens for analysis, and let X be the r.v. denoting the number of specimens of rock R1 selected for analysis.

(i) Specify the p.d.f. of the r.v. X.

(ii) What is the probability that at least 10 specimens of the rock R₁ are included in the analysis?

(iii) What is the probability that all specimens come from the rock R²?

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