MathDB
Expected Value of Heads after Three Flips

Source: 2015 amc 10b #18

February 26, 2015
probabilityexpected valueAMC

Problem Statement

Johann has 6464 fair coins. He flips all the coins. Any coin that lands on tails is tossed again. Coins that land on tails on the second toss are tossed a third time. What is the expected number of coins that are now heads? <spanclass=latexbold>(A)</span>32<spanclass=latexbold>(B)</span>40<spanclass=latexbold>(C)</span>48<spanclass=latexbold>(D)</span>56<spanclass=latexbold>(E)</span>64<span class='latex-bold'>(A) </span> 32 \qquad<span class='latex-bold'>(B) </span> 40 \qquad<span class='latex-bold'>(C) </span> 48 \qquad<span class='latex-bold'>(D) </span> 56 \qquad<span class='latex-bold'>(E) </span> 64