The Croupier Says Yes

A croupier rolls a fair six-sided die behind a screen. You may ask her one yes/no question, and she answers truthfully with probability 34 \frac{3}{4} and lies (states the opposite) with probability 14 \frac{1}{4} , independent of the roll. You ask whether the die landed on six, and she answers yes. What is the probability the die actually shows a six?

Answer

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