Explanation:

- In the examination, 47% of students passed in science.

- Therefore, 53% failed in science.

- 51% of students failed in mathematics.

- Also, 42% failed in both science and mathematics.

- To find out how many passed in both subjects, use the formula for the union of two sets:

$$

P(\text{pass in science} \cup \text{pass in mathematics}) = P(\text{pass science}) + P(\text{pass math}) - P(\text{pass both})

$$

- Rearrange and substitute known values:

$$

P(\text{pass both}) = P(\text{pass science}) + P(\text{pass math}) - P(\text{pass science} \cup \text{pass math})

$$

- Using complements:

- Pass in one is Fail in the other: $$

P(\text{pass both}) = (1 - 0.53) + (1 - 0.51) - (1 - 0.42)

$$

- Calculate:

$$

P(\text{pass both}) = 0.47 + 0.49 - 0.58 = 0.38 \text{ or } 38\%

$$

- Options are:

- Option 1: 36%

- Option 2: 40%

- Option 3: 38%

- Option 4: 42%