Example of binomial distribution, Mathematics

Assignment Help:

Example: Joanne is given a four-question multiple-choice quiz.  She hasnt studied the material to be quizzed, so she decides to answer the questions by randomly guessing the answers without reading the questions or the answers. 

Answer Sheet for Quiz

Directions: Circle the best answer to each question.

1. A B C D E
2. A B C D E
3. A B C D E
4. A B C D E

1. What is the probability that Joanne answered all of the questions correctly?
2. What is the probability that Joanne chose wrong answers for all of the questions?

Solution:

Let X be the number of correct answers on the quiz.  Then X can be 0, 1, 2, 3, or 4.  Since each question has five possible answers and only one correct answer, the probability of choosing the correct answer for a question is 1/5.  The probability of choosing the incorrect answer is 4/5.

P(X = 4) is the probability that all of the questions were answered correctly. The events are independent because each question is separate event.

P(X = 0) is the probability that all of the questions were answered incorrectly. 1153_Example of binomial distribution.gif

This tree diagram shows all of the possible outcomes for this experiment as well as the difference values of the random variable.

494_Example of binomial distribution2.gif

From this diagram, you can see that there are four occurrences of one correct answer (X = 1).  We can list all of the remaining probabilities with the help of the tree diagram.

499_Example of binomial distribution3.png

In general: 
P(X = x) is the product of three factors:

1. The number of ways that exactly X successes can occur in a set of n trials.
2. The probability of having X successes.
3. The probability that failure will occur the remaining (n'X) trials.


Related Discussions:- Example of binomial distribution

Find intervals while function is increasing or decreasing, Find out all int...

Find out all intervals where the given function is increasing or decreasing. f ( x ) = - x 5 + 5/2 x 4 + 40/3 x 3 + 5 Solution To find out if the function is increasi

More optimization problems, More Optimization Problems Example   A w...

More Optimization Problems Example   A window is being built in which the bottom is rectangle and the top is a semicircle. If there framing materials is 12 meters what have

Variation, If p=10 when q=2,find p when q=5

If p=10 when q=2,find p when q=5

Lines, i dont understand angels and lines

i dont understand angels and lines

Ratios, a muffin recipe calls for three forth of a cup of sugar and one eig...

a muffin recipe calls for three forth of a cup of sugar and one eight of a cup of butter. travis accidentally put in one whole cup of butter. how much sugar does travis need to put

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Calculus, The law of cosines can only be applied to acute triangles. Is thi...

The law of cosines can only be applied to acute triangles. Is this true or false?

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

Ratios, What is the ratio of the cone''s volume to the cylinder''s volume

What is the ratio of the cone''s volume to the cylinder''s volume

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd