Question

Tiana's Cupcakes recorded how many cupcakes it recently sold in each flavor.
lemon cupcakes 50
chocolate cupcakes 313
coconut cupcakes 91
vanilla cupcakes 66
peanut butter cupcakes 5
What is the experimental probability that the next cupcake sold will be a coconut cupcake?
Write your answer as a fraction or whole number.
P(coconut cupcake)=

Answer 1

To find the experimental probability that the next cupcake sold will be a coconut cupcake, we first need to determine the total number of cupcakes sold.

Here's the breakdown of the sales:

- Lemon cupcakes: 50
- Chocolate cupcakes: 313
- Coconut cupcakes: 91
- Vanilla cupcakes: 66
- Peanut butter cupcakes: 5

Now, we sum these numbers:

\[
50 + 313 + 91 + 66 + 5 = 525
\]

The total number of cupcakes sold is 525.

Next, we look at the number of coconut cupcakes sold, which is 91.

The probability \( P \) of selling a coconut cupcake is given by the formula:

\[
P(\text{coconut cupcake}) = \frac{\text{Number of coconut cupcakes sold}}{\text{Total number of cupcakes sold}} = \frac{91}{525}
\]

Thus:

\[
P(\text{coconut cupcake}) = \frac{91}{525}
\]

This fraction can be simplified by finding the greatest common divisor of 91 and 525.

The prime factorization of 91 is \( 7 \times 13 \).

The prime factorization of 525 is \( 3 \times 5^2 \times 7 \).

The common factor is 7.

Now, divide both the numerator and the denominator by 7:

\[
\frac{91 \div 7}{525 \div 7} = \frac{13}{75}
\]

Therefore, the simplified probability is:

\[
P(\text{coconut cupcake}) = \frac{13}{75}
\]