Onamultiple-choiceexam,with k possibleresponsesforeachquestion,astudentknowsthe answerwithprobability and hastoguesstheanswerrandomlywithprobability (1). Given that astudentcorrectlyanswersaquestion,findtheprobabilitytheytrulyknewtheanswer. Evaluatetheexpressionyouderivewhen k = 5 and

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Onamultiple-choiceexam,with k possibleresponsesforeachquestion,astudentknowsthe answerwithprobability π and hastoguesstheanswerrandomlywithprobability (1−π). Given that astudentcorrectlyanswersaquestion,findtheprobabilitytheytrulyknewtheanswer.

Evaluatetheexpressionyouderivewhen k = 5 and π is (i)0.90,(ii)0.10.

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