To find the probability that both fruits Sharon takes are apples, we can use the concept of combinations.
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Total number of fruits: There are 5 apples and 3 pears, so the total number of fruits in the basket is:
\[ 5 + 3 = 8 \text{ fruits} \]
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Total ways to choose 2 fruits from 8: The number of ways to choose any 2 fruits from 8 is given by the combination formula \( \binom{n}{r} \):
\[ \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28 \]
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Ways to choose 2 apples from 5: The number of ways to choose 2 apples from the 5 available is:
\[ \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]
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Calculating the probability: The probability that both fruits chosen are apples is the number of ways to choose 2 apples divided by the total number of ways to choose 2 fruits:
\[ P(\text{both apples}) = \frac{\text{Number of ways to choose 2 apples}}{\text{Total ways to choose 2 fruits}} = \frac{10}{28} \]
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Simplifying the fraction: We can simplify \( \frac{10}{28} \):
\[ \frac{10}{28} = \frac{5}{14} \]
Thus, the probability that both fruits chosen are apples is:
\[ \boxed{\frac{5}{14}} \]