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If 3 students are selected randomly, what is the probability?

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Final answer:

The probability of a student randomly guessing more than 75% of the answers correctly on a 32-question exam with each question having three possible choices is extremely low, almost close to zero.

Step-by-step explanation:

The question on the probability that a student guesses more than 75 percent of the questions correctly on a multiple choice exam with three possible answers for each of the 32 questions involves calculating the probability of a binomial random variable being above a certain value. Since there are no shortcuts for large calculations like this (without the use of technology such as a TI-83 or 84 calculator), we would typically use a binomial probability formula or binomial distribution calculations.

However, the probability of getting a score that high by random guessing is extremely small, since the expected number of questions guessed correctly by chance would be 32/3, or about 10.67 questions, which is far less than 75% of 32 (which is 24). Thus, without going into the complex calculations, we can assert that the probability is very close to zero.

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