Answer:
0.0138
Explanation:
The probability of getting exactly 4 questions right by guessing can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials (17 questions), k is the number of successes (4 correct answers), p is the probability of success on a single trial (1/5 for guessing), and (n choose k) is the binomial coefficient.
Plugging in the values, we get:
P(X = 4) = (17 choose 4) * (1/5)^4 * (4/5)^13
P(X = 4) ≈ 0.0138 (rounded to four decimal places)
Therefore, the probability that the student will get exactly 4 questions right by guessing is approximately 0.0138.