Three coins are on a table,tails side up,yen picks one at random with equal probability on each and turns it over,on average,how many times should she do this in order to get three heads up?
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Answer:10. Solution:Let an denote the expected number of moves needed to finish when n coins are still tails sideup.Therefore,wehave a0=0.Then,when n>0,we note that there is an 3 chance to turn up a coin that is currently tails and thereby subtract 1 from the number of coins that are currently tails sideup,and a 1−n 3 to add 1 to the number of coins that are currently tails sideup.Thus,we have the following system of equation in four variables: a0=0 a1=1+1 3 a2=1+2 3 a3=1+a2 Solving,wegeta1=7,a2=9,anda3=10.
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