2015 AMC 10B Problems/Problem 18

Problem

Johann has $64$ 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?

$\textbf{(A) } 32 \qquad\textbf{(B) } 40 \qquad\textbf{(C) } 48 \qquad\textbf{(D) } 56 \qquad\textbf{(E) } 64$

Solution

The expected number of heads on the first flip is $32$ , on the second flip is is $16$ , and on the third flip it is $8$ . Adding these gives $\boxed{\mathbf{(D)}\ 56}$

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2015 AMC 10B Problems/Problem 18

Problem

Solution