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
Which function is a quadratic function? c(x) = 6x + 3x3 d(x) = x – 8x4 p(x) = –5x – x2 k(x) = 2x2 + 9x4
Citrus2011 [14]
Easy
quadratic means 2nd degree

means highest power of exponent is 2
so like x^2

first one
we have 3x^3, that is 3rd degree,nope

2nd one
we have 8x^4, nope, that is 4th degree

3rd one
we have -x^2, yep

4th one, we have 9x^4, that is 4th degree

answer is 3rd one or p(x)=-5x-x^2
7 0
3 years ago
Read 2 more answers
Which expression is equivalent to: <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B200%7D" id="TexFormula1" title="\sqrt[3]{2
Alja [10]

Answer:

The answer is b.

2 \sqrt[3]{25}

7 0
3 years ago
Read 2 more answers
The ratio of men to women working for a company is 2 to 3 . If there are 120 employees total, how many women work for the compan
gtnhenbr [62]
I think the answer is 20
3 0
3 years ago
Write the quadratic function f(x) = x2 + 8x + 3 in vertex form.​
Stolb23 [73]
F(x)=(x+4)2−13 i think this is the simplified of the perfect trinomial
6 0
3 years ago
What is the value of 0.6 + 0.3? Write your answer as a fraction in lowest terms
Allisa [31]
9/10 i the answer i believe
3 0
3 years ago
Other questions:
  • At a private​ school, each​ first-year student is sorted into one of four houses. If 3 students are randomly selected from 11 av
    6·1 answer
  • Approximate ∛-25 to the nearest tenth.
    5·2 answers
  • What is the answer??
    9·1 answer
  • Geometry help please!
    14·1 answer
  • What is 13 in radical fraction form
    6·1 answer
  • Answer pls thanks uuuuu
    5·1 answer
  • What the coordinates of the midpoint of (2,4) and (3,5) ​
    10·1 answer
  • Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals
    12·1 answer
  • 2/7 divided by 3/4 in simplest form
    11·1 answer
  • Can somebody answer this
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!