A multiple choice exam has 10 questions. Each question has 4 possible answers, of which only 1 is correct. If a student guesses on each question, what is the probability that the student will get exactly 6 questions correct?

Step 1 ：Step 1: Identify the values for the formula of binomial distribution. In this case, n (number of trials) is 10, k (number of successes) is 6, and p (probability of success on a single trial) is 0.25 (since there's 1 correct answer out of 4).

Step 2 ：Step 2: Plug these values into the formula for the binomial probability: \(P(X=k) = C(n, k) * p^k * (1-p)^{n-k}\)

Step 3 ：Step 3: Calculate the binomial coefficient C(n, k) which is \(C(10, 6) = \frac{10!}{6!(10-6)!} = 210\)

Step 4 ：Step 4: Calculate \(p^k = (0.25)^6 = 0.000244140625\)

Step 5 ：Step 5: Calculate \((1-p)^{n-k} = (0.75)^4 = 0.31640625\)

Step 6 ：Step 6: Multiply all these values together to find the probability: \(P(X=6) = 210 * 0.000244140625 * 0.31640625 = 0.01614\)