# math-Probablity

posted by .

A student is writing a multiple choice test consisting of 40 questions, each of which provides four possible choices. He is certain that he has 16 questions correct. If he guesses for all of the remaining 24 questions, what is the probability that he will pass the test?

• math-Probablity -

Assuming that a pass is getting at least 20 of the 40 correct ....
What the student CANNOT have is
zero of the remaining 24 correct : C(24,0) (1/4)^0 (3/4)^24 = .001003391
1 of the remaining 24 correct : C(24,1) (1/4) (3/4)^23 = .00802713
2 of the remaining 24 correct : C(24,2) (1/4)^2 (3/4)^22 = .030770665
3 of the remaining 24 correct : C(24,3) (1/4)^3 (3/4)^21 = .075217183

prob he will pass = 1 - (sum of the above 4 cases)
= ...

check my arithmetic

• math-Probablity -

Assuming:
1. he got indeed the 16 questions correctly.
2. the remaining 24 answers were random choices
3. there was exactly one correct answer

to each of the remaining questions
then he will need 4 more correct answers to get 50%.
Let
p=probability of guessing a question correctly = 0.25
q=1-p=probability of guessing incorrectly = 0.75

The probability of getting 0 to 3 correct guesses (i.e. fail) is
C(24,0)*q^24*p*0 +
C(24,1)*q^23*p*1 +
C(24,2)*q^22*p*2 +
C(24,3)*q^21*p*3
=0.0010+0.0080+0.00308+0.00752
=0.1150
where C(n,r)=n!/((n-r)!r!)
Therefore the probability that he will pass (at 50%) is
1-0.1150=0.8850

• To Reiny: great minds... -

Here we go again!

• math-Probablity -

What is the probability of that ? lol

## Similar Questions

1. ### Stats

An instructor gives a test with 20 multiple choice questions. There are 4 responses per questions and only one choice correct. The test also has 30 True/False questions. Determine the probability a student randomly guessing on all …
2. ### math

A multiple-choice test has 10 questions. Each question has 5 choices. If a student answers each question by guessing randomly, find the probability that the student gets: a) at most 4 questions correct b) at least 7 questions correct …
3. ### stats

a student randomly guesses at five multiple-choice questions, each question has five possible choices (suppose the choice for each question is independent): a) Find the probability that the student gets exactly three correct. b) What …

suppose a student takes a multiple choice test with 10 questions. suppose each question has 4 possible answers. if the student guesses randomly on each questions,what is the probability that the student gets exactly 6 correct?

If a student randomly guesses at 15 multiple-choice questions, find the probability that the student gets exactly seven correct. Each question has four possible choices
6. ### pro

A student has taken an exam consisting 10 multiple choice questions. Each question has 4 answer choices and has one correct answer. Questions are independent of each other. If the student answer questions randomly, what is the probability …
7. ### statistics

A math test consists of 17 multiple choice questions, each with five possible answers (a, b, c, d, e), only one of which is correct. Assume that a student takes the test and randomly answers the questions. What is the probability that …
8. ### Statistics

An unprepared student is about to take his first test of the semester. He is told that his test will be composed of 20 multiple choice questions, each with 4 possible answers, only one of which is correct. a.What is the probability …
9. ### Finite

Assume that the test has 5 true/false questions, and 10 multiple choice questions (4 options per questions), each with exactly one correct answer. If a student guesses randomly on each question, what is his expected score?
10. ### math

You are writing multiple choice test. Each question has 5 choices, only one of which is correct. You have no idea how to answer three questions. What is the probability that you will get all three of these questions correct if you …

More Similar Questions