Answer: 1/3
Explanation:
In a multiple-choice examination with 3 choices for each question, the probability of guessing the correct answer is 1/3. Since you are trying to guess exactly 6 of 10 answers correctly, this means that you will be guessing incorrectly on 4 of the 10 questions. The probability of guessing incorrectly on a single question is 2/3.
To find the probability of guessing exactly 6 of 10 answers correctly, we can use the binomial probability formula, which is given by the following expression:
P(x) = (n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
In this formula, n is the total number of trials, x is the number of successes, p is the probability of success on a single trial, and 1-p is the probability of failure on a single trial.
Plugging in the values for this problem, we get:
P(6) = (10!/(6!(10-6)!) * (1/3)^6 * (2/3)^4
= 210 * (1/3)^6 * (2/3)^4
= 210 * (1/3^6) * (2/3^4)
= 210 * (1/3^6) * (1/3^2)
= 210 * (1/3^8)
= 210 * (1/6561)
= 0.0322
So the probability of guessing exactly 6 of 10 answers correctly in a multiple-choice examination with 3 choices for each question is approximately 0.0322, or about 3.22%.