Question
There are two multiple choice questions on a quiz, one with four answer choices and one with six answer choices. Suppose the probability of a student answering the questions correctly is 3/12. Are the events independent? Use the probability of crazy event to support the answer.
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Answer to a math question There are two multiple choice questions on a quiz, one with four answer choices and one with six answer choices. Suppose the probability of a student answering the questions correctly is 3/12. Are the events independent? Use the probability of crazy event to support the answer.
Madelyn
4.786 Answers
Let's denote the event of a student answering the first question correctly as A and the event of a student answering the second question correctly as B.
The probability of a student answering each question correctly is P(A) = P(B) = 3/12 = 1/4.
If events A and B are independent, then the joint probability of both events occurring is equal to the product of their individual probabilities:
P(A and B) = P(A) * P(B)
Since the events A and B are independent, the joint probability of the student answering both questions correctly is:
P(A and B) = (1/4) * (1/4) = 1/16
However, the probability of a student answering the questions correctly is given as 3/12, which is greater than 1/16. This violation of the multiplication rule for independent events implies that the events A and B are not independent.
Therefore, the events of a student answering two multiple-choice questions correctly are not independent.
\textbf{Answer:} The events of a student answering the two multiple-choice questions correctly are not independent.
The probability of a student answering each question correctly is P(A) = P(B) = 3/12 = 1/4.
If events A and B are independent, then the joint probability of both events occurring is equal to the product of their individual probabilities:
P(A and B) = P(A) * P(B)
Since the events A and B are independent, the joint probability of the student answering both questions correctly is:
P(A and B) = (1/4) * (1/4) = 1/16
However, the probability of a student answering the questions correctly is given as 3/12, which is greater than 1/16. This violation of the multiplication rule for independent events implies that the events A and B are not independent.
Therefore, the events of a student answering two multiple-choice questions correctly are not independent.
\textbf{Answer:} The events of a student answering the two multiple-choice questions correctly are not independent.
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