If-the-ratio-of-the-students-that-pass-a-test-to-those-that-fail-is-in-ratio-4-1-If-9-students-were-chosen-at-random-what-is-the-probability-that-exactly-7-passed-the-test-

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Question Number 12156 by tawa last updated on 15/Apr/17

$$\mathrm{If}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{students}\mathrm{that}\mathrm{pass}\mathrm{a}\mathrm{test}\mathrm{to}\mathrm{those}\mathrm{that}\mathrm{fail}\mathrm{is}\mathrm{in}\mathrm{ratio}4:1,$$$$\mathrm{If}9\mathrm{students}\mathrm{were}\mathrm{chosen}\mathrm{at}\mathrm{random},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{probability}\mathrm{that}\mathrm{exactly}$$$$7\mathrm{passed}\mathrm{the}\mathrm{test}.$$

Answered by mrW1 last updated on 23/Apr/17

$$probabilitypasstestp=\frac{4}{4+1}=0.8$$$$probabilityfailq=1-0.8=0.2$$$$$$$$C_7^9\times 0.8^7\times 0.2^2=36\times 0.8^7\times 0.2^2$$$$=0.302=30.2\mathrm{\%}$$

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