1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Neporo4naja [7]
3 years ago
8

In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz

at all, and decides to randomly guess the answers. (Round your answers to four decimal places.)
(a) What is the probability that the first question she gets right is the second question?
(b) What is the probability that she gets exactly 1 or exactly 2 questions right?
(c) What is the probability that she gets the majority of the questions right?
Mathematics
1 answer:
Ahat [919]3 years ago
6 0

Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a \frac{1}{4} = 0.25 probability of getting ir right. So \pi = 0.25. There are five questions, so n = 5.

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

So

P = 0.75(0.25) = 0.1875

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: P = P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955

P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637

P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

P = P(X = 3) + P(X = 4) + P(X = 5)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 3) = C_{5,3}.(0.25)^{3}.(0.75)^{2} = 0.0879

P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146

P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001

P = P(X = 3) + P(X = 4) + P(X = 5) = 0.0879 + 0.0146 + 0.001 = 0.1035

There is a 10.35% probability that she gets the majority of the questions right.

You might be interested in
A room that is 5 meters long has an area
Sveta_85 [38]

Answer:

Breadth=x+2

Step-by-step explanation:

Solution,\\\\Length(l)=5m\\\\Area=5x+10m^{2} \\\\Breadth(b)=?\\\\As,\\\\Area=l*b\\\\5x+10=5*b\\\\b=\frac{5x+10}{5}\\\\b=\frac{5x}{5} +\frac{10}{5} \\\\b=x+2

7 0
2 years ago
a radio station can broadcasts in all directions to a distance of 60 mi. what is the area in which the station can be heard
zaharov [31]

Answer:

Area = PI * radius ^ 2

Area = PI * 60^2

Area = PI * 3,600

Area = 11,309.73 square miles

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The endpoints of the diameter of a circle are (−2, −3) and (4, −1). Which equation represents the circle?
Alika [10]

Answer:

The equation of circle is (x-1)^{2}+(y-2)^{2} = 18

Step-by-step explanation:

Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)

We know that the equation of circle is

(x-h)^{2} + (y-k)^{2}= r^{2}

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

(  \frac{x1+x2}{2} , \frac{y1+y2}{2}  )

( \frac{-2+4}{2} , \frac{-3-1}{2}  )

(1,2)

Hence (h,k) is (1,2)

Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get

(4-1)^{2} +(-1-2)^{2} = r^{2}

r^{2} = 18

Now substituting values of (h,k) and r^{2} in equation of circle, we get

(x-1)^{2}+(y-2)^{2} = 18

Hence the equation of circle is (x-1)^{2}+(y-2)^{2} = 18

5 0
3 years ago
Read 2 more answers
Given that x = 1, y = -2, z = 3, find the value of:
yarga [219]
You have to plug in the given numbers and perform each operation. Let me know if you have questions. The answers are circled.

6 0
3 years ago
$4,600 invested in a CD paying the investor 5% annual return for one year?<br><br> what’s the answer
xxMikexx [17]

Answer:

230

Step-by-step explanation:

multiply 6,400 by 5% then multiply that by the 1 year and 230 will be the answer

Hope this helps :)

7 0
3 years ago
Other questions:
  • 4 square root 5 is equivalent to
    9·1 answer
  • What is the area of a triangle with vertices at (−4, 1) , ​ (−7, 5) ​ , and ​ (0, 1) ​ ? Enter your answer in the box. ___units²
    14·2 answers
  • What is two more than the product of five and four ? (Explain how you got your answer)
    15·2 answers
  • 35 POINTS WILL MARK BRAINLIEST the area of a base of a square notepad is 9 square inches. What is the length of one side of the
    11·2 answers
  • The line passes through the point (4,2) and has slope of -1
    12·1 answer
  • On page number 3 Q1 AND Q2 I NEED THE ANSWER PLS HELP ME OUT<br>LOOK IN THE PDF AND GO TO PAGE 3
    7·1 answer
  • PLEASE ASNWER ASASP for BRAINLEST!!!!!!!!!!!!!!!!!
    13·1 answer
  • Write 0.851 as a fraction in simplest form.
    14·1 answer
  • PLEASE Help me what is -6(4x-1/3y)
    13·1 answer
  • Here’s the <br> question to my last <br> post :) <br><br> anyways
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!