Questions: According to a study, 83% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 83%, 13 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is (Round to three decimal places as needed.)

According to a study, 83% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 83%, 13 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum.

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is
(Round to three decimal places as needed.)
Transcript text: According to a study, $83 \%$ of $\mathrm{K}-12$ schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these $83 \%, 13$ out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Determine the Probability of Using Digital Content

According to the study, the probability that a randomly selected K-12 school or district uses digital content is given by:

\[ P(D) = 0.83 \]

where \( P(D) \) is the probability of using digital content.

Step 2: Calculate the Probability of Using Digital Content in Curriculum

Out of the schools that use digital content, \( 13 \) out of \( 20 \) use it as part of their curriculum. Therefore, the conditional probability that a school uses digital content as part of their curriculum given that it uses digital content is:

\[ P(C|D) = \frac{13}{20} = 0.65 \]

where \( P(C|D) \) is the probability of using digital content in the curriculum.

Step 3: Calculate the Joint Probability

To find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum, we use the multiplication rule of probabilities:

\[ P(D \cap C) = P(D) \cdot P(C|D) = 0.83 \cdot 0.65 \]

Calculating this gives:

\[ P(D \cap C) = 0.5395 \]

Step 4: Round the Result

Rounding the result to three decimal places, we find:

\[ P(D \cap C) \approx 0.539 \]

Final Answer

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is:

\[ \boxed{0.539} \]

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