A bag contains solid-color marbles, of which some are red and the rest are blue. A random sample of 16 marbles is selected from the bag, and 3 of the 16 marbles are red. If the bag contains 192 marbles, what is the most reasonable estimate for the number of red marbles in the bag?

Rationale

36 is the most reasonable estimate for the number of red marbles in the bag.

To find the estimated number of red marbles in the bag, we can set up a proportion based on the sample. With 3 red marbles in a sample of 16, we can extrapolate this ratio to the total of 192 marbles, leading us to estimate approximately 36 red marbles in the bag.

A (12) YOUR ANSWER

This choice represents a significantly lower estimate than what the data suggests. If there were only 12 red marbles in a total of 192, the proportion of red marbles would be only 12/192, equating to just 1 red marble in every 16 marbles, which does not align with the observed sample of 3 red marbles out of 16.

B (18) YOUR ANSWER

While this option is higher than 12, it remains too low based on the sample. An estimation of 18 red marbles would yield a proportion of 18/192, suggesting roughly 0.9 red marbles per sampled group of 16, which again does not match the actual sample ratio of 3 red marbles.

C (31) YOUR ANSWER

This choice is closer to our expected estimate but still falls short. A proportion of 31 red marbles would result in about 31/192, translating to approximately 1.6 red marbles per 16. This does not accurately reflect the observed ratio of 3 red marbles in the sample, indicating a conservative estimate.

D (36) CORRECT

Estimating 36 red marbles leads to a proportion of 36/192, or 1 red marble in every 5.33 marbles. This aligns closely with the sample observation of 3 out of 16, which suggests that the bag likely contains a higher number of red marbles than the lower options provide.

Conclusion

The estimation for the number of red marbles in the bag should align with the observed sample ratio. Given that 3 out of 16 marbles were red, extrapolating this proportion to a total of 192 marbles results in a reasonable estimate of 36 red marbles. This choice accurately reflects the sample data, making it the most plausible answer among the options provided.

A bag contains solid-color marbles, of which some are red and the rest are blue. A random sample of 16 marbles is selected from the bag, and 3 of the 16 marbles are red. If the bag contains 192 marbles, what is the most reasonable estimate for the number of red marbles in the bag?

36 is the most reasonable estimate for the number of red marbles in the bag.

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