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URL: https://nakafa.com/en/exercises/high-school/snbt/mathematical-reasoning/try-out/2026/set-2/10

Exercises: Try Out 2026 - Set 2: Real exam simulation to sharpen your skills and build confidence. - Question 10

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## Exercise 10

### Question

export const metadata = {
  title: "Question 10",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "01/31/2026",
};

There are two boxes containing balls of different colors. The first box contains <InlineMath math="4" /> red balls and <InlineMath math="3" /> blue balls. The second box contains <InlineMath math="7" /> red balls and <InlineMath math="3" /> white balls. One ball is taken from each box. The probability of drawing a red ball from the first box and a white ball from the second box is....


### Choices

- [ ] $$\frac{3}{70}$$
- [ ] $$\frac{7}{20}$$
- [x] $$\frac{12}{70}$$
- [ ] $$\frac{17}{20}$$
- [ ] $$\frac{61}{70}$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Question 10",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "01/31/2026",
};

**Analyzing Probability for the First Box**

In the first box, there are a total of <InlineMath math="4 + 3 = 7" /> balls. We want to draw a red ball, of which there are <InlineMath math="4" />. The probability of drawing a red ball from the first box is:

<MathContainer>
  <BlockMath math="P(\text{Red}_1) = \frac{n(\text{Red}_1)}{n(S_1)} = \frac{4}{7}" />
</MathContainer>

**Analyzing Probability for the Second Box**

In the second box, there are a total of <InlineMath math="7 + 3 = 10" /> balls. We want to draw a white ball, of which there are <InlineMath math="3" />. The probability of drawing a white ball from the second box is:

<MathContainer>
  <BlockMath math="P(\text{White}_2) = \frac{n(\text{White}_2)}{n(S_2)} = \frac{3}{10}" />
</MathContainer>

**Calculating the Combined Probability**

Since drawing balls from the two boxes are **independent events** (the event in the first box does not affect the second box), the probability of both events occurring together is calculated by multiplying their individual probabilities.

<MathContainer>
  <BlockMath math="P(\text{Total}) = P(\text{Red}_1) \times P(\text{White}_2)" />
  <BlockMath math="P(\text{Total}) = \frac{4}{7} \times \frac{3}{10}" />
  <BlockMath math="P(\text{Total}) = \frac{12}{70}" />
</MathContainer>

Thus, the probability of drawing a red ball from the first box and a white ball from the second box is <InlineMath math="\frac{12}{70}" />.


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