# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/9

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Construction Probability

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## Exercise 9

### Question

export const metadata = {
  title: "Construction Probability",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Suppose a contractor is going to build an apartment. The probability of a public protest occurring is <InlineMath math="0.7" />. If there is no protest, the probability that the construction finishes on time is <InlineMath math="0.8" />. If there is a protest, the probability that the construction finishes on time is <InlineMath math="0.4" />.

Determine the probability that the construction finishes on time!


### Choices

- [x] $$0.52$$
- [ ] $$0.62$$
- [ ] $$0.65$$
- [ ] $$0.68$$
- [ ] $$0.70$$

### Answer & Explanation

export const metadata = {
  title: "Construction Probability Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Defined:

-   <InlineMath math="A =" /> event construction finishes on time
-   <InlineMath math="A^c =" /> event construction does not finish on time
-   <InlineMath math="B =" /> event a protest occurs
-   <InlineMath math="B^c =" /> event no protest occurs
-   <InlineMath math="A|B =" /> event construction finishes on time given a protest
-   <InlineMath math="A|B^c =" /> event construction finishes on time given no protest

The probability that construction finishes on time is the sum of the probability of a protest multiplied by the probability of finishing on time given a protest, plus the probability of no protest multiplied by the probability of finishing on time given no protest.

<MathContainer>
  <BlockMath math="P(A) = P(B)P(A|B) + P(B^c)P(A|B^c)" />
</MathContainer>

We know that:

<MathContainer>
  <BlockMath math="P(B) = 0.7, \quad P(B^c) = 1 - 0.7 = 0.3" />
</MathContainer>

<MathContainer>
  <BlockMath math="P(A|B^c) = 0.8, \quad P(A|B) = 0.4" />
</MathContainer>

Then:

<MathContainer>
  <BlockMath math="P(A) = (0.7)(0.4) + (0.3)(0.8)" />
</MathContainer>

<MathContainer>
  <BlockMath math="P(A) = 0.28 + 0.24 = 0.52" />
</MathContainer>

Thus, the probability that the construction finishes on time is <InlineMath math="0.52" />.


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