. A student is preparing for an upcoming exam. The professor for the course has

Question

. A student is preparing for an upcoming exam. The professor for the course has given the class 25
questions to study from and plans to select 10 of the questions for use on the actual exam. Suppose the
student knows how to solve 20 of the 25 questions.
a) What is the probability that the student will get perfect on the test?
b) What is the probability that the student will get at least 8 questions correct on the test?
c) What’s the probability that the students passes the test?

this is all the information that is given.

Explanation / Answer

all possible questions sets 25C10

student will get perfevt score if any 10 of those 20 come in exam

so prob(perfect score)=20C10/25C10=0.05652174

Prob(atleast 8 questions correct)=p(8 questions correct)+p(9 questions correct)+p(10 questions correct)=(20C8 * 5C2 +20C9 *5C1 +20C10)/25C10= 0.6988142

here to be noted that number of correct questions follows hypergeometric distribution

assuming that if the number of corrext questions in greater than 5 then student passes

because in any case student will do 5 sums correctly

so p(x>5)=1-p(x=5)= 0.9952569

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.