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Question Number 133696 by Mikael_786 last updated on 23/Feb/21

A test consists of four questions  each of which contains five alternative  answers, one of which is correct.  The test pass condition is at least  four correct answers. A student, not  knowing the test subject, scored the  answers randomly.How is the  probability for the student to pass?

$$\mathrm{A}\:\mathrm{test}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{four}\:\mathrm{questions} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{contains}\:\mathrm{five}\:\mathrm{alternative} \\ $$$$\mathrm{answers},\:\mathrm{one}\:\mathrm{of}\:\mathrm{which}\:\mathrm{is}\:\mathrm{correct}. \\ $$$$\mathrm{The}\:\mathrm{test}\:\mathrm{pass}\:\mathrm{condition}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{four}\:\mathrm{correct}\:\mathrm{answers}.\:\mathrm{A}\:\mathrm{student},\:\mathrm{not} \\ $$$$\mathrm{knowing}\:\mathrm{the}\:\mathrm{test}\:\mathrm{subject},\:\mathrm{scored}\:\mathrm{the} \\ $$$$\mathrm{answers}\:\mathrm{randomly}.\mathrm{How}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{for}\:\mathrm{the}\:\mathrm{student}\:\mathrm{to}\:\mathrm{pass}? \\ $$

Answered by Ar Brandon last updated on 23/Feb/21

((1/5))^4

$$\left(\frac{\mathrm{1}}{\mathrm{5}}\right)^{\mathrm{4}} \\ $$

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