In a class of 30 students, 18 are enrolled in a math course, and 12 are enrolled in a science course. Among the students enrolled in the science course, 8 are also enrolled in the math course. What is the probability that a student is enrolled in the math course given that they are enrolled in the science course?

Rationale

0.67

To find the probability that a student is enrolled in the math course given that they are enrolled in the science course, we use the formula for conditional probability. The number of students enrolled in both courses is 8, and the total number of students in the science course is 12. Thus, the probability is calculated as 8 divided by 12, which simplifies to \( \frac{2}{3} \) or approximately 0.67.

A (0.27) YOUR ANSWER

This value does not accurately reflect the conditional probability of being enrolled in the math course given enrollment in the science course. The calculation based on the provided data shows a much higher probability.

B (0.4) YOUR ANSWER

This option misrepresents the ratio of students enrolled in both courses compared to the total number of science course students. The computation should yield a probability based on the 8 students enrolled in both courses out of 12 total science students, which is not equal to 0.4.

C (0.44) YOUR ANSWER

This choice is also incorrect as it does not correspond to the correct fraction derived from the enrollment figures. The actual calculation yields a probability of 0.67, making 0.44 an inaccurate representation of the scenario.

D (0.67) CORRECT

This choice correctly represents the probability that a student is enrolled in the math course given that they are enrolled in the science course. With 8 students in both courses out of 12 science students, the probability simplifies to \( \frac{8}{12} \), which equals 0.67.

Conclusion

In summary, the probability that a student is enrolled in the math course given that they are also enrolled in the science course is 0.67. This is determined by the ratio of students enrolled in both courses to the total number of students in the science course. The other options do not align with the correct calculation based on the given data.

0.67

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