A multiple-choice test has 48 questions, each with four
response choices. If a student is simply guessing at the
answers,
a. What is the probability of guessing correctly for
any question?
b. On average, how many questions would a student
get correct for the entire test?
c. What is the probability that a student would get
more than 15 answers correct simply by guessing?
d. What is the probability that a student would get 15
or more answers correct simply by guessing?
15
To answer these questions, we need to understand the concept of probability and apply it to the given information.
a. What is the probability of guessing correctly for any question?
Since each question has four response choices, the probability of guessing correctly for any question is 1 out of 4 choices or 1/4.
b. On average, how many questions would a student get correct for the entire test?
To find the average number of questions a student would get correct, we multiply the probability of guessing correctly for any question by the total number of questions. So, the average number of questions a student would get correct is (1/4) * 48 = 12.
c. What is the probability that a student would get more than 15 answers correct simply by guessing?
To find the probability of getting more than 15 answers correct, we need to calculate the probability of getting exactly 16, 17, 18, ..., 48 answers correct and then sum them up.
The probability of getting exactly k correct answers out of 48 questions can be calculated using the binomial probability formula:
P(X = k) = (nCk) * (p^k) * (q^(n-k))
where n is the total number of trials (48 questions), p is the probability of success (1/4), q is the probability of failure (3/4), and (nCk) is the binomial coefficient, also known as "n choose k".
By calculating the probabilities for each value of k from 16 to 48, and then summing them up, we can find the probability of getting more than 15 answers correct by guessing.
d. What is the probability that a student would get 15 or more answers correct simply by guessing?
Similar to the previous question, we need to calculate the probabilities of getting exactly 15, 16, 17, ..., 48 answers correct and then sum them up.