Question
Question 1: You take a statistics exam. The test is a multiple choice questionnaire comprising 7 independent questions. Each question has 9 possible answers, 3 of which are correct. A student is considered to have answered a question correctly if and only if all 3 correct answers have been selected. You will pass the exam if you answer at least 4 questions correctly. We assume that for each question you randomly choose 3 answers. You answer the first question of the exam by randomly choosing 3 answers. What is the probability that you chose all 3 correct answers?
183
likes915 views
Answer to a math question Question 1: You take a statistics exam. The test is a multiple choice questionnaire comprising 7 independent questions. Each question has 9 possible answers, 3 of which are correct. A student is considered to have answered a question correctly if and only if all 3 correct answers have been selected. You will pass the exam if you answer at least 4 questions correctly. We assume that for each question you randomly choose 3 answers. You answer the first question of the exam by randomly choosing 3 answers. What is the probability that you chose all 3 correct answers?
Lurline
4.6107 Answers
Let's calculate the probability of choosing all 3 correct answers on the first question:
The total number of ways to choose 3 answers from 9 possible answers is given by the combination formula:
\text{Total possible ways}=\binom{9}{3}=\frac{9!}{3!\left(9-3\right)!}
The number of ways to choose all 3 correct answers is 1, as there is only one correct combination of 3 answers out of the 9:
\text{Number of correct ways} = 1
Therefore, the probability of choosing all 3 correct answers on the first question is:
\text{Probability}=\dfrac{\text{Number of correct ways}}{\text{Total possible ways}}=\dfrac{1}{\frac{9!}{3!\left(9-3\right)!}}
\text{Probability}=\dfrac{1}{\frac{9!}{3!\left(9-3\right)!}}=\dfrac{1}{84}
\boxed{\text{Probability} = \dfrac{1}{84}}
The total number of ways to choose 3 answers from 9 possible answers is given by the combination formula:
The number of ways to choose all 3 correct answers is 1, as there is only one correct combination of 3 answers out of the 9:
Therefore, the probability of choosing all 3 correct answers on the first question is:
Frequently asked questions (FAQs)
Math question: Given a right triangle with one leg measuring 5 units and the hypotenuse measuring 13 units, find the length of the other leg.
+
Math question: In a circle, if the angle at the center is 60°, what is the measure of the angle at the circumference, in degrees?
+
Question: What is the period of the trigonometric function f(x) = 3sin(5x) - cos(2x)?
+
New questions in Mathematics