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 the square root of x, multiplied by the cube root of y, raised to the power of z?
+
What is the value of f(x) = 3x^2 + 2x - 1 when x = 4?
+
What is the equation of the exponential function shown in the graph: y = 2^x, where x represents the input value and y represents the output value?
+
New questions in Mathematics