To find the cubic polynomial \( f(x) = ax^3 + bx^2 + cx + d \), we use the given conditions to set up a system of equations:
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- Probability: $ \frac{16}{20} = \frac{4}{5} $.
- Thus, the probability is $\boxed{\dfrac{4}{5}}$.Question:
- Find the cubic polynomial \( f(x) \) such that \( f(1) = 3 \), \( f(2) = -1 \), \( f(3) = 2 \), and \( f(4) = 5 \).
- \( f(1) = a(1)^3 + b(1)^2 + c(1) + d = 3 \), which simplifies to:
- a + b + c + d = 3
- \( f(2) = a(2)^3 + b(2)^2 + c(2) + d = -1 \), which simplifies to:
