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To find the experimental probability that the next hat requested will be a turban, we need to calculate the number of turban hats that have been requested so far.
Rebecca lent out 6 turban hats out of a total of 6 + 3 + 3 + 2 = 14 hats.
Therefore, the experimental probability of the next hat requested being a turban is 6/14 or simplifying to 3/7.
So, the answer is 3/7.