SEstudent22
New member
- Joined
- Jul 25, 2021
- Messages
- 10
Here is the problem: "A student is taking an exam. The exam has 15 questions. Every question is multiple-choice and has 4 answers, out of which only one is correct. The student passes the exam with a 10 (the highest grade) if he answers at least 90% of the questions correctly. What is the probability that the student will pass the exam with a 10 if the answers are chosen randomly?"
There are 15 questions with 4 answers each, there is only one answer. So there is a 1/4 (0.25) chance that the student will answer the question correctly.
I define the following event:
A - the student passes the exam with a 10.
We are searching for P(A).
I define a random variable:
X - number of correct answers.
The student needs to answer at least 90% of the questions correctly to pass with a 10.
90% of 15 is 13.5 ( I round it up to 14 since we can't have 13 and a half questions answered).
P(A) = P{X≥14} = P{X=14} + P{X=15}
I believe that X has a binomial distribution for n=15 and p=0.25 so this is my answer:
[math]\binom{15}{14}*0.25^{14}*0.75^1 + \binom{15}{15}*0.25^{15}*0.75^0[/math]
However, the final probability I get is really really low, so I doubt that this is the correct answer... Could somebody please review my work and tell me the flaw in my thinking?
There are 15 questions with 4 answers each, there is only one answer. So there is a 1/4 (0.25) chance that the student will answer the question correctly.
I define the following event:
A - the student passes the exam with a 10.
We are searching for P(A).
I define a random variable:
X - number of correct answers.
The student needs to answer at least 90% of the questions correctly to pass with a 10.
90% of 15 is 13.5 ( I round it up to 14 since we can't have 13 and a half questions answered).
P(A) = P{X≥14} = P{X=14} + P{X=15}
I believe that X has a binomial distribution for n=15 and p=0.25 so this is my answer:
[math]\binom{15}{14}*0.25^{14}*0.75^1 + \binom{15}{15}*0.25^{15}*0.75^0[/math]
However, the final probability I get is really really low, so I doubt that this is the correct answer... Could somebody please review my work and tell me the flaw in my thinking?
