Final answer:
The probability that the student will answer a randomly selected question correctly on a multiple-choice exam with 30 questions is a weighted sum of the certain answers and the guessed ones. The calculation shows a probability of 0.706(6), which does not match any of the provided options a-d, suggesting there may be an error in the question or the answer choices.
Step-by-step explanation:
The probability that the student answers the question correctly on a multiple-choice exam with 30 questions, each having 5 answer choices can be found by considering two scenarios. First, the questions he already knows the answers to, and second, the questions he guesses on.
Step 1: Calculate known answers probability
For the 19 questions that the student knows, the probability of answering correctly is 1 (since he knows the answer).
Step 2: Calculate guessed answers probability
For the remaining 11 questions, the probability of guessing an answer correctly is 1/5 or 0.2 since there are 5 possible choices for each question.
Step 3: Calculate overall probability
The total probability that the student answers a randomly selected question correctly is the weighted sum of both scenarios. This can be calculated as:
Probability = (19/30) * 1 + (11/30) * 1/5
Probability = 19/30 + 11/30 * 1/5
Probability = 19/30 + 11/150
Probability = (95 + 11) / 150
Probability = 106/150
Probability = 0.706(6)
Thus, the correct answer is none of the options provided (a-d). It appears there might have been an error in the question or answer choices.