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

likes
915 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?

Expert avatar
Lurline
4.6
107 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}}

Frequently asked questions (FAQs)
Math question: Find the amplitude, period, phase shift, and range of the sine function f(x) = sin x.
+
Math Question: What is the slope-intercept equation of a line passing through the points (2, 4) and (6, 10)? Answer using the y = mx + b form. (
+
Find the roots of the cubic equation x^3 - 5x^2 + 3x + 2 = 0.
+
New questions in Mathematics
Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.
5(4x+3)=75
what is 3% of 105?
a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?
2. Juan is flying a piscucha. He is releasing the thread, having his hand at the height of the throat, which is 1.68 meters from the ground, if the thread forms an angle of elevation of 50°, at what height is the piscucha at the moment that Juan has released 58 meters of the thread?
If eight basketball teams participate in a tournament, find the number of different ways that first, second, and third places can be decided assuming that no ties are allowed.
The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?
What is the r.p.m. required to drill a 13/16" hole in mild steel if the cutting speed is 100 feet per minute?
4. Show that if n is any integer, then n^2 3n 5 is an odd integer
Desarrolla (2x)(3y + 2x)5
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one
Let X be a discrete random variable such that E(X)=3 and V(X)=5. Let 𝑌 = 2𝑋^2 − 3𝑋. Determine E(Y).
Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·s.
solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0
if y=1/w^2 yw=2-x; find dy/dx
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?
A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.