Rebecca supplies costumes to a number of theater companies and recently lent out a number of different hats.

\begin{tabular}{|l|l|}
\hline
Turbans & 6 \\
\hline
Berets & 3 \\
\hline
Mortarboards & 3 \\
\hline
Top hats & 2 \\
\hline
\end{tabular}

What is the experimental probability that the next hat requested from Rebecca's inventory will be a turban?

Write your answer as a fraction or whole number.

[tex]$\square$[/tex]



Answer :

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]