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Question Number 24490 by FilupES last updated on 19/Nov/17
I hold my hand behind my back, and secretly  hold up n fingers (0≤n≤5).     I then as you, am I holding up k fingers?  Where k is also a random number 0≤k≤5.     You randomly guess Yes or No.  What is the probability you guess correctly?
$$\mathrm{I}\:\mathrm{hold}\:\mathrm{my}\:\mathrm{hand}\:\mathrm{behind}\:\mathrm{my}\:\mathrm{back},\:\mathrm{and}\:\mathrm{secretly} \\ $$$$\mathrm{hold}\:\mathrm{up}\:{n}\:\mathrm{fingers}\:\left(\mathrm{0}\leqslant{n}\leqslant\mathrm{5}\right). \\ $$$$\: \\ $$$$\mathrm{I}\:\mathrm{then}\:\mathrm{as}\:\mathrm{you},\:\mathrm{am}\:\mathrm{I}\:\mathrm{holding}\:\mathrm{up}\:{k}\:\mathrm{fingers}? \\ $$$$\mathrm{Where}\:{k}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{random}\:\mathrm{number}\:\mathrm{0}\leqslant{k}\leqslant\mathrm{5}. \\ $$$$\: \\ $$$$\mathrm{You}\:\mathrm{randomly}\:\mathrm{guess}\:\mathrm{Yes}\:\mathrm{or}\:\mathrm{No}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{you}\:\mathrm{guess}\:\mathrm{correctly}? \\ $$
Commented by prakash jain last updated on 20/Nov/17
1/6?
$$\mathrm{1}/\mathrm{6}? \\ $$
Commented by FilupES last updated on 20/Nov/17
I honestly don′t know.     The question has been bugging me.
$$\mathrm{I}\:\mathrm{honestly}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}. \\ $$$$\: \\ $$$$\mathrm{The}\:\mathrm{question}\:\mathrm{has}\:\mathrm{been}\:\mathrm{bugging}\:\mathrm{me}. \\ $$

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