# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/11

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 11

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## Exercise 11

### Question

export const metadata = {
  title: "Problem 11",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

The probabilities of Ali, Bima, and Dika passing the National Exam are <InlineMath math="0.75" />, <InlineMath math="0.8" />, and <InlineMath math="0.85" /> respectively.

The probability that only one person passes among the three is...


### Choices

- [ ] $$0.085$$
- [x] $$0.095$$
- [ ] $$0.85$$
- [ ] $$0.95$$
- [ ] $$0.075$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 11",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Let:
-   <InlineMath math="P(A)" /> = Probability Ali passes
-   <InlineMath math="P(B)" /> = Probability Bima passes
-   <InlineMath math="P(D)" /> = Probability Dika passes

Given:

<MathContainer>
  <BlockMath math="P(A) = 0.75 \rightarrow P(A^c) = 1 - 0.75 = 0.25" />
  <BlockMath math="P(B) = 0.8 \rightarrow P(B^c) = 1 - 0.8 = 0.2" />
  <BlockMath math="P(D) = 0.85 \rightarrow P(D^c) = 1 - 0.85 = 0.15" />
</MathContainer>

If only one person passes, there are three mutually exclusive possibilities:

#### Ali passes, Bima and Dika fail

<MathContainer>
  <BlockMath math="P(A) \cdot P(B^c) \cdot P(D^c) = 0.75 \cdot 0.2 \cdot 0.15" />
  <BlockMath math="= 0.0225" />
</MathContainer>

#### 2. Bima passes, Ali and Dika fail

<MathContainer>
  <BlockMath math="P(B) \cdot P(A^c) \cdot P(D^c) = 0.8 \cdot 0.25 \cdot 0.15" />
  <BlockMath math="= 0.03" />
</MathContainer>

#### Dika passes, Ali and Bima fail

<MathContainer>
  <BlockMath math="P(D) \cdot P(A^c) \cdot P(B^c) = 0.85 \cdot 0.25 \cdot 0.2" />
  <BlockMath math="= 0.0425" />
</MathContainer>

#### Total Probability

Thus, the probability that only one person passes is the sum of these three possibilities:

<MathContainer>
  <BlockMath math="0.0225 + 0.03 + 0.0425 = 0.095" />
</MathContainer>


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