three coins problem!
Level
pending
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?
The answer is 10.
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1 solution
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.
Credits from emc.