SOLUTION: A student takes a 20 question, multiple choice exam with 5 choices for each question. If the student is guessing, find the following probabilities: A. Getting less than 5 question

Algebra ->  Probability-and-statistics -> SOLUTION: A student takes a 20 question, multiple choice exam with 5 choices for each question. If the student is guessing, find the following probabilities: A. Getting less than 5 question      Log On


   

Question 463713: A student takes a 20 question, multiple choice exam with 5 choices for each question. If the student is guessing, find the following probabilities:
A. Getting less than 5 questions right?
B. Passing the exam with at least an 80% score?
C. Getting every question but 2 wrong?
Please help?!?
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = number of correct answers in a 20-multiple choice questions.
X~Binomial(n=20, p=0.2)
There are 5 choices so the probability of success is 1/5 or 0.2 and the probability of failure is 1-0.2 = 0.8.
Therefore, the pmf of X is p%28x%29+=+%28matrix%282%2C1%2C+20%2C+x%29%29%2A%280.2%29%5Ex%2A%280.8%29%5E%2820-x%29
Using the pmf we can now solve problems A,B, and C.
A. = 0.6296
B. 80% of 20 is 16 so we compute , the result is a very small number close to zero.
C. p%2818%29+=+%28matrix%282%2C1%2C+20%2C+18%29%29%2A%280.2%29%5E18%2A%280.8%29%5E2, the result is also a very small number close to zero.