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.
107
likes535 views
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.
Frequently asked questions (FAQs)
What is the product of 15 and 7?
+
What is the limit of (2x^3 + 5x^2 - x) / (x^2 - 3) as x approaches 2?
+
What is the average score of a group of students if 5 students scored 80, 90, 95, 85, and 75?
+
New questions in Mathematics