Question: Bethany has a fair six-sided die (with sides 1... 6). Angelica has a fair coin, with 1 on one side and 4 on the other

Bethany has a fair six-sided die (with sides 1... 6). Angelica has a fair coin, with "1" on one side and "4" on the other side. Each day, Bethany rolls the die one time, and Angelica flips the coin one time (the results are independent). Let N denote the first day on which Bethany's die has a strictly larger result than Angelica's coin. Let X denotes the value of Bethany's die on 'day N. Find the expected value of X.

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