Mining for crystals is a hobby for some, and even a profession for many. Both amateur and professional crystal hunters go digging in search for samples that they suspect to be crystals, and then they test the samples to verify their claims. After testing, the samples are labelled as Precious, Semi-precious, or Unverified. For each type of samples (Precious, Semi-precious, and Unverified) respectively, 12%, 26%, and 23% of them are formed at the surface level; while for the same, 35%, 39%, and 54% are formed underground. The remaining samples are formed under the ocean floor. Experience says that while mining, Precious, Semi-precious, and Unverified samples are found in a ratio of 3:9:28. If a particular sample was separately tested six times, and was determined to be formed under the ocean in two of the tests, what is the probability that the sample was Semi-precious?

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The probability of being formed under the ocean in two of the tes... View the full answer