Solve simple compound probability and counting problems using organized reasoning.
Find expected successes for a compound event
Problem
A game uses \(\text{one}~\text{coin}~\text{flip}\) and \(\text{one}~\text{number}~\text{cube}\) numbered \(1~\text{to}~6\) for each play. You win if the coin shows heads and the number cube shows an even number. If the game is played \(48~\text{times}\), about how many wins would you expect?
Big Picture
What this problem is really about
Separate this into probability first and expectation second. Find the chance of heads and the chance of an even cube result, multiply because both independent conditions must occur, and then scale that win probability by the number of plays. The final count is a long-run expectation, not a guarantee for one set of games.
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