document.write( "Question 1178261: Roll a die once. Then roll it as many times as the outcome from the first roll. Getting the special number \"3\" on any roll means a win. What is the expected number of wins from this experiment? \n" ); document.write( "

Algebra.Com's Answer #813985 by robertb(5830) $\"\"$ $\"About$

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Let X = r.v. equal to the value of the die on the 1st throw.\r
\n" ); document.write( "\n" ); document.write( "Then for X = 1, 2, 3, 4, 5, 6, it can be shown combinatorially that $\"P%28X+=+x%29+=+1%2F6%5E2+%2B+5%2F6%5E3+\"$ +...+ $\"5%5E%28x-1%29%2F6%5E%28x%2B1%29+=+%281%2F6%29%2A%281-%285%2F6%29%5Ex%29\"$ . \r
\n" ); document.write( "\n" ); document.write( "The probability of a '3' turning up on any throw is 1/6. Hence the expectation for the number of wins in this game is \r
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to 2 d.p.\r
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