When I throw 2 fair coins, the most likely outcome is that they will give 1 head and 1 tail.
So on average, I will need to throw 2 fair coins to get at least 1 head and at least 1 tail?
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It is impossible to get one head and one tail on only one throw, so you have to throw at least two coins to get the desired result. However, it is not guaranteed to happen in two throws; indeed, it will only happen half the time. Thus, half the time you must throw more than twice, so the average number of throws must be greater than two.