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Answer :
Final answer:
This question is about binomial probability. You apply the binomial probability formula replacing respective values to get the probability.
Explanation:
This problem falls under the subject of probability in mathematics, specifically binomial probability.
In the context, each question in the test is an independent event with two possible outcomes, a right or wrong answer. Since each question has 5 options and only one is correct, the probability of answering a question correctly by random guessing is 1/5 = 0.2. And, the probability of a wrong answer is 1- 0.2 = 0.8.
The formula for binomial probability is: P(X = k) = C(n, k) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.
Applying this formula to our problem:
- n (number of trials) = 10
- k (number of successes) = 4
- p (probability of success) = 0.2
- q (probability of failure) = 0.8
Substituting these values into the formula, we can calculate the probability. Note that C(n, k) is the combinatorics function which calculates the number of ways k successes can occur in n trials.
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Final answer:
The question involves working out the chances of correctly guessing answers to a multiple-choice test using the binomial probability formula. The formula will take into account the total number of questions, the probability of correctly guessing an answer, and the number of successes sought.
Explanation:
This is a problem of calculating a probability related to multiple independent events. The subject matter is machine learning, but understanding that is not necessary to solve this. We'll be using the binomial probability formula, which is P(k;n,p) = C(n, k) * (p) ^ k * (1 - p) ^ (n - k).
Here, n is the total number of trials - in this case, the number of questions, which is 10. p is the probability of success in a given trial, which is to answer a question correctly. Since there is 1 correct answer out of 5 options, p is 1/5. And we are looking for the probability of k successes - in this case, 4 correct answers.
So plug in the values into C(n, k) * (p) ^ k * (1 - p) ^ (n - k). After doing the required calculations, you'll get the probability that the student will get exactly 4 correct answers without knowing anything about machine learning.
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