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
Ugo [173]
3 years ago
8

1. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge

of the correct answers to any of the questions. She has decided on a strategy
in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball
for each question and replaces the ball in the box.


The marking on the ball will determine her answer
to the question. There are five multiple choice questions on the exam. What is the probability that she will get:

a. Five questions correct?

b. At least four questions correct?

c. No questions correct?

d. No more than two questions correct?
Mathematics
1 answer:
LenKa [72]3 years ago
3 0

Answer:

a) 0.001 = 0.1% probability that she will get five questions correct.

b) 0.0156 = 1.56% probability that she will get at least four questions correct.

c) 0.2373 = 23.73% probability that she will get no questions correct.

d) 0.8965 = 89.65% probability that she will get no more than two questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she gets it correct, or she does not. The probability of getting a question correct is independent of any other question, which means that the binomial probability distribution is used to solve this question.

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}.p^{x}.(1-p)^{n-x}

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

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

And p is the probability of X happening.

There are five multiple choice questions on the exam.

This means that n = 5

She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box.

This means that p = \frac{1}{4} = 0.25

a. Five questions correct?

This is P(X = 5). So

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

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

0.001 = 0.1% probability that she will get five questions correct.

b. At least four questions correct?

This is:

P(X \geq 4) = P(X = 4) + P(X = 5)

So

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

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(X \geq 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.001 = 0.0156

0.0156 = 1.56% probability that she will get at least four questions correct.

c. No questions correct?

This is P(X = 0). So

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

P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373

0.2373 = 23.73% probability that she will get no questions correct.

d. No more than two questions correct?

This is:

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2). So

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

P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373

P(X = 1) = C_{5,0}.(0.25)^{1}.(0.75)^{4} = 0.3955

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

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965

0.8965 = 89.65% probability that she will get no more than two questions correct.

You might be interested in
Order the expressions from least value to greatest value.
pashok25 [27]

Answer:

I think the answer is the first one.

7 0
3 years ago
Compare the dotplot to a histogram of the data. (Select all that apply.)
Aleks04 [339]

Answer:

(B) The raw data can be retrieved from the dot plot, but not the histogram.

(C) Dot plots show the frequency of individual data values.

Step-by-step explanation:

There are two correct answers:

(B) The raw data can be retrieved from the dot plot, but not the histogram.

(C) Dot plots show the frequency of individual data values.

Dot plots are used for small data sets where values fall into a number of categories, unlike histograms.

8 0
3 years ago
Please help!!!! I am bad at math
zhannawk [14.2K]
1:Correct
2: 8 / 2 = 4
3: 6 / 2 = 3
4: 6*1*6 = 36
5: 0/6 + 6 = 6
6: 5+3+1+9 = 18
8 0
2 years ago
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angl
nirvana33 [79]

The equation that solve for x is as follows;

70 + 60 + x = 180

<h3 /><h3>How to find an angle?</h3>

The equation that can be used to find the measure of angle x can be found as follows:

60 + 70 + y = 180

Therefore,

130 + y = 180

subtract 130 from both sides

130 - 130 + y = 180 - 130

y = 50°

70 + 60 + x = 180

130 + x = 180

x = 180 - 130

x = 50°

x and y are  vertically opposite angles.

learn  more on angles here: brainly.com/question/24460838

#SPJ1

4 0
1 year ago
1 question, 10 POINTS ( no rude answers please )
klemol [59]
I believe the answer is 54%.

Hope this helps!
8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the estimate of 242-220
    10·2 answers
  • HELP ASAP
    6·1 answer
  • (5 , 1 ) , ( − 2 , b ) = √ 85 find the value of b
    10·2 answers
  • Eric is hanging a rectangle mirror that has a diagonal of 47 inches with an angle of depression of 60°. How many square inches i
    15·2 answers
  • Ling is 1 year less than twice as old as his sister. If the sum of their ages is 14 years how old is Ling
    10·1 answer
  • What is 3 to the power of three halves equal to?
    12·1 answer
  • What is the value of -d when d = -2?
    15·1 answer
  • Find the sum or difference.
    10·1 answer
  • Solve for x. 42-3x=30.<br> Please and thank you!<br> will mark brainliest!
    6·2 answers
  • My question is in the picture
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!