a student prepares for an exam by studying a list of 10 different problems. she can solve 6 of the problems…

a student prepares for an exam by studying a list of 10 different problems. she can solve 6 of the problems. for the exam, the instructor selects 5 questions at random from the list of 10.\n- how many different exams can the instructor give?\n- what is the probability that the student can solve all 5 problems?\n- what is the probability that the student can solve exactly 4 problems?\n- what is the probability that the student can solve at least 1 problem?\n- what is the probability that the student can solve at least 1 problem?

a student prepares for an exam by studying a list of 10 different problems. she can solve 6 of the problems. for the exam, the instructor selects 5 questions at random from the list of 10.\n- how many different exams can the instructor give?\n- what is the probability that the student can solve all 5 problems?\n- what is the probability that the student can solve exactly 4 problems?\n- what is the probability that the student can solve at least 1 problem?\n- what is the probability that the student can solve at least 1 problem?

Answer

Answer:

  • How many different exams can the instructor give?: (C(10,5)=\frac{10!}{5!(10 - 5)!}=252)
  • What is the probability that the student can solve all 5 problems?: (\frac{C(6,5)}{C(10,5)}=\frac{6}{252}=\frac{1}{42})
  • What is the probability that the student can solve exactly 4 problems?: (\frac{C(6,4)\times C(4,1)}{C(10,5)}=\frac{15\times4}{252}=\frac{60}{252}=\frac{5}{21})
  • What is the probability that the student can solve at least 1 problem?: (1-\frac{C(4,5)}{C(10,5)}=1 - 0 = 1)