Probability a student passes a test?

There are five multiple choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one option per question is correct. Suppose the student guesses the answer to each question, and his or her guesses from question to question are independent. If the student needs at least 20 points to pass the test, the probability that the student passes is closest to


A. 0.0146


B. 0.0010


C. 0.0156





I tried using the mutiplication rule for independent event using the probablity of getting one question right as .5 and multiply 4X and times .75 as the probabilty of getting a ? wrong... what am i doing wrong?

Probability a student passes a test?
The answer is C. 0.0156





Let X be the number of questions answered correctly. Then X follows a binomial distribution with parameters p=0.25 and n=5.





In order to score at least 20 points the student needs to answer 4 or 5 questions correctly.





P(passing) = P(X=4) + P(X=5) = 5!/(4!1!) 0.25^4 0.75^1 + 5!/(5!0!) 0.25^5 0.75^0 = 0.0156.





The reason that p=0.25 is that for each question there are 4 possible responses but only one correct response and 1/4 = 0.25.





You need to consider the different combinations of getting 4 correct (e.g. getting the first 4, missing the last vs. missing the first one but getting the last 4 correct...)
Reply:at least 20 points means that student must get at least 4 answers right.





the probability of getting a right answer is 1/4


the proablilit of getting a wrong answer is 3/4





P = P(4) + P(5)





P(4) = 5C4 (1/4)^4 (3/4)





the reason you have 5C4, because the student can get ANY 4 out of 5 answers right





P(5) = (1/4)^5





P = 5C4 (1/4)^4 (3/4) + (1/4)^5


P = 0.0156 %26lt;== answer





it's C





hope it helps
Reply:The probability of each question right isn't 0.5 (1 out of 2) but 0.25 (1 out of 4) because there are 4 choices (a, b, c, d). Thus, the odds at the student getting each question right is 0.25. But the student needs four questions right, so we expect that to happen





0.25 * 0.25 * 0.25 * 0.25 percent of the time, which equals


.0039. That's the closes to (B), or .001
Reply:the probability of getting the question right is not .5 its .25 try that out. and dont use the fact tha u have to 25% chance of getting the right answer and u need to get 4 out of 5 questions right.
Reply:There is a 20% chance the student will guess the right answer.


He must get at least four of the questions correct to pass the test.


I took 20%^4 = 0.0016