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There are 6 blue chips in the bag.

Given that the probability of selecting a red chip is 3/5, we can determine the number of red chips in the bag. If there are 15 chips total, this means there are 9 red chips (since 3/5 of 15 is 9). Therefore, the number of blue chips, which is the total number of chips minus the number of red chips, is 15 - 9 = 6.

A) 2

This option is incorrect because if there were only 2 blue chips, the number of red chips would have to be 13. The probability of selecting a red chip in that case would be 13/15, which does not match the given probability of 3/5.

B) 3

This option is also incorrect. If there were 3 blue chips, then the number of red chips would be 12. The probability of selecting a red chip would then be 12/15, simplifying to 4/5, which again does not align with the given probability of 3/5.

C) 6

This option is correct. With 6 blue chips, there are 9 red chips (15 total - 6 blue). The probability of selecting a red chip from the bag is then 9/15, which simplifies to 3/5, matching the condition given in the problem.

D) 9

This option is incorrect because if there were 9 blue chips, then there would only be 6 red chips. The probability of selecting a red chip would be 6/15, simplifying to 2/5, which does not correspond to the stated probability of 3/5.

E) 12

This option is incorrect. If there were 12 blue chips, that would leave only 3 red chips. The probability of selecting a red chip in this scenario would be 3/15, simplifying to 1/5, which does not match the required probability of 3/5.

Conclusion

The correct answer is C, as it accurately reflects the number of blue chips based on the given probability of selecting a red chip. All other options fail to meet the probability criteria stipulated in the question, thus confirming that C is the only valid solution.