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counting and probability intermediate

Problem

Johann has 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?
(A)
(B)
(C)
(D)
Solution
We can simplify the problem first, then apply reasoning to the original problem. Let's say that there are coins. Shaded coins flip heads, and blank coins flip tails. So, after the first flip; Then, after the second (new heads in blue); And after the third (new head in green); So in total, of the coins resulted in heads. Now we have the ratio of of the total coins will end up heads. Therefore, we have
Final answer
D