Rolling a die to size the next die

EasyConditional Probability & Expectation Expected Value~3m

You roll a fair standard $6$ -sided die and observe $k$ . You then roll a fair $(6+k)$ -sided die (faces $1, 2, \dots, 6+k$ ) and record its value. What is the expected value of the second roll?

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Given first roll $k$ , the second die is uniform on $1..6{+}k$ , mean $(7+k)/2$ .
Average that over $k=1..6$ using $\mathbb{E}[k]=3.5$ .

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5.25

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Rolling a die to size the next die

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