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Question Number 133021 by liberty last updated on 18/Feb/21

A multiple −choice quiz has 200  questions each with 4 possible   answers of which only 1 is the correct  answer . What is the probability   that sheer guesswork yields   from 25 to 30 correct answer for  80 of the 200 problems about which  the student has no knowledge?

$$\mathrm{A}\:\mathrm{multiple}\:−\mathrm{choice}\:\mathrm{quiz}\:\mathrm{has}\:\mathrm{200} \\ $$$$\mathrm{questions}\:\mathrm{each}\:\mathrm{with}\:\mathrm{4}\:\mathrm{possible}\: \\ $$$$\mathrm{answers}\:\mathrm{of}\:\mathrm{which}\:\mathrm{only}\:\mathrm{1}\:\mathrm{is}\:\mathrm{the}\:\mathrm{correct} \\ $$$$\mathrm{answer}\:.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\: \\ $$$$\mathrm{that}\:\mathrm{sheer}\:\mathrm{guesswork}\:\mathrm{yields}\: \\ $$$$\mathrm{from}\:\mathrm{25}\:\mathrm{to}\:\mathrm{30}\:\mathrm{correct}\:\mathrm{answer}\:\mathrm{for} \\ $$$$\mathrm{80}\:\mathrm{of}\:\mathrm{the}\:\mathrm{200}\:\mathrm{problems}\:\mathrm{about}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{student}\:\mathrm{has}\:\mathrm{no}\:\mathrm{knowledge}?\: \\ $$

Answered by bemath last updated on 19/Feb/21

P(25≤X≤30)=Σ_(x=25) ^(30) b(x,80,(1/4))

$$\mathrm{P}\left(\mathrm{25}\leqslant\mathrm{X}\leqslant\mathrm{30}\right)=\underset{\mathrm{x}=\mathrm{25}} {\overset{\mathrm{30}} {\sum}}\mathrm{b}\left(\mathrm{x},\mathrm{80},\frac{\mathrm{1}}{\mathrm{4}}\right) \\ $$

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