To find the theoretical probability that Chandra will be chosen as one of the four participants from the group of five students (Adriana, Ben, Chandra, Diana, and Ernesto), we can follow these steps:
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Total outcomes: The total number of ways to choose 4 students from 5 can be calculated using the combination formula \( C(n, k) = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of items to choose from, and \( k \) is the number of items to choose.
Here, \( n = 5 \) and \( k = 4 \).
\[ C(5, 4) = \frac{5!}{4!(5-4)!} = \frac{5!}{4! \cdot 1!} = \frac{5 \times 4!}{4! \times 1} = 5 \]
So there are 5 possible combinations of students.
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Favorable outcomes: To count the number of favorable outcomes where Chandra is one of the chosen students, we need to choose 3 more students from the remaining 4 students (Adriana, Ben, Diana, and Ernesto).
The number of ways to choose 3 students from these 4 is:
\[ C(4, 3) = \frac{4!}{3!(4-3)!} = \frac{4!}{3! \cdot 1!} = 4 \]
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Calculating the probability: The probability \( P \) that Chandra is chosen can be calculated by dividing the number of favorable outcomes by the total outcomes:
\[ P(\text{Chandra is chosen}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{5} \]
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Convert to percentage: To express this as a percentage,
\[ \frac{4}{5} = 0.8 \] Thus, \( 0.8 \times 100% = 80% \).
The theoretical probability that Chandra will be chosen as one of the science fair participants is 80%.