To determine the experimental probability that the next pie sold will be a cherry pie, we can follow these steps:
1. Identify the number of cherry pies sold: According to the information provided, Aubrey's Pie Shop sold 6 cherry pies.
2. Identify the number of other pies sold: It is also given that 14 other pies were sold.
3. Calculate the total number of pies sold: The total number of pies sold is the sum of cherry pies and other pies.
[tex]\[
\text{Total pies} = \text{Number of cherry pies} + \text{Number of other pies} = 6 + 14 = 20
\][/tex]
4. Determine the experimental probability of selling a cherry pie next: The probability of selling a cherry pie is the ratio of the number of cherry pies sold to the total number of pies sold.
[tex]\[
P(\text{cherry pie}) = \frac{\text{Number of cherry pies}}{\text{Total pies}} = \frac{6}{20}
\][/tex]
5. Simplify the fraction (if needed): Simplify [tex]\(\frac{6}{20}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{6}{20} = \frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\][/tex]
So, the experimental probability that the next pie sold will be a cherry pie is:
[tex]\[
P(\text{cherry pie}) = \frac{3}{10}
\][/tex]
