To determine the fraction of cookies that are both chocolate flavored and have sprinkles, we can break this down step by step.
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Let's denote the total number of cookies in the bakery as \( C \).
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According to the problem, half of the cookies are chocolate flavored: \[ \text{Number of chocolate flavored cookies} = \frac{1}{2}C \]
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It is given that \( \frac{4}{5} \) of the chocolate flavored cookies also have sprinkles. Therefore, we can calculate the number of chocolate flavored cookies that have sprinkles: \[ \text{Number of chocolate flavored cookies with sprinkles} = \frac{4}{5} \times \frac{1}{2}C = \frac{4}{10}C = \frac{2}{5}C \]
To find the fraction of the total cookies that are both chocolate flavored and have sprinkles, we use the total number of cookies \( C \) as the base:
\[ \text{Fraction of cookies that are chocolate flavored and have sprinkles} = \frac{\frac{2}{5}C}{C} = \frac{2}{5} \]
Thus, the fraction of cookies that are both chocolate flavored and have sprinkles is \( \frac{2}{5} \).
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