To determine the experimental probability that the next hat requested from Rebecca's inventory will be a turban, we need to follow these steps:
1. Calculate the total number of hats lent out.
Rebecca has lent out the following:
- Turbans: 6
- Berets: 3
- Mortarboards: 3
- Top hats: 2
Adding these together, we find the total number of hats lent out:
[tex]\[
6 + 3 + 3 + 2 = 14
\][/tex]
2. Determine the number of turbans.
From the table, we know that Rebecca lent out 6 turbans.
3. Calculate the experimental probability of requesting a turban.
The experimental probability is found by dividing the number of favorable outcomes (requesting a turban) by the total number of possible outcomes (total hats lent out). Thus, the probability [tex]\(P(\text{turban})\)[/tex] is:
[tex]\[
P(\text{turban}) = \frac{\text{Number of turbans}}{\text{Total number of hats}} = \frac{6}{14}
\][/tex]
4. Simplify the fraction if possible.
The fraction [tex]\(\frac{6}{14}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{6 \div 2}{14 \div 2} = \frac{3}{7}
\][/tex]
Therefore, the experimental probability that the next hat requested from Rebecca's inventory will be a turban is:
[tex]\[
\boxed{\frac{3}{7}}
\][/tex]
