Problem #7: A geologist has collected 22 specimens of basaltic rock and and 17 s

Question

Problem #7: A geologist has collected 22 specimens of basaltic rock and and 17 specimens of granite. The geologist instructs a laboratory assistant to randomly select 7 of the specimens for analysis. (a) What is the probability that at least 3 of the selected specimens are granite? (b) What is the expected number of granite specimens in the sample? (c) If this same process is repeated every day, how many days (on average) will it take before getting a sample consisting entirely of granite? Problem #7(a): Problem #7(b) Problem #7(c): 1 round your answer to the nearest integer

Explanation / Answer

Total number of besaltic rock specimen = 22

Granite specimen = 17

(A) Total specimen selected = 7

so Pr(At least 3 would be graanite) = 1 - Pr(Granite = 2) - Pr(Granite =1) - Pr( Granite =0)

= 1 - [17C222C5 + 17C122C6 + 17C022C7] / 39C7

= 1 - (5020389/ 15380937) = 0.6736

(b) Expected Number of granite specimens in the sample = 17 * 7 / (22 + 17) = 3.0512

(C) Probability of getting a sample entirely of granite Pr( Granite = 7) = 17C7 * 22C0 / 39C7 = 0.0012644

so Expected number of days to get a sample entrely of Granite = 1/0.0012644 = 791 (in integer)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.