Final answer:
The probability of getting more than 3 questions correct by guessing on a 5-question multiple-choice test with 4 answer choices involves calculating the sum of the probabilities for getting exactly 4 and exactly 5 questions right using the binomial probability formula.
Step-by-step explanation:
The question asks to find the probability that a student who is guessing will get more than 3 questions correct on a 5-question, multiple-choice test with 4 options for each question. To calculate this, we consider the probability for exactly 4 and exactly 5 correct guesses. Since the student is guessing, the probability of getting any one question right is 1/4, and getting it wrong is 3/4.
To find the probability of getting exactly 4 questions right, we use the binomial probability formula: P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k), where 'n' is the number of trials, 'k' is the number of successes, and 'p' is the probability of success on a single trial. Hence, P(4 right) = (5 choose 4) * (1/4)^4 * (3/4)^1. Likewise, to find the probability of getting all 5 questions right, P(5 right) = (5 choose 5) * (1/4)^5 * (3/4)^0, since there are no wrong answers in this scenario. The total probability of getting more than 3 questions right is the sum of the two probabilities: P(more than 3 right) = P(4 right) + P(5 right).