Question 1207541: A test consists of 10 multiple choice questions, each with five possible answers. one of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test.
Answer by ikleyn(52799)   (Show Source):
You can put this solution on YOUR website! .
A test consists of 10 multiple choice questions, each with five possible answers.
one of which is correct. To pass the test a student must get 60% or better on the test.
If a student randomly guesses, what is the probability that the student will pass the test.
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This experiment is a binomial distribution with 10 trials.
The probability of success in each individual trial is 1/5 = 0.2;
the probability of fault is 4/5 = 0.8.
They want you determine the probability of 6 or more successes of 10 trials.
You may calculate P(6), P(7), P(8), P(9) and P(10) separately and then add.
It is really tedious exercise. Another way is to calculate this probability in one click,
using an Excel function BINOM.DIST in the accumulative mode
P = P(6) + P(7) + P(8) + P(9) + P(10) = 1 - BINOM.DIST(5, 10, 0.2, 1) = 0.006369. ANSWER
Notice that we need P = P(6) + P(7) + P(8) + P(9) + P(10), and we calculate it as
the COMPLEMENT of BINOM.DIST(5, 10, 0.2, 1) to 1:
P(6) + P(7) + P(8) + P(9) + P(10) = 1 - (P(0) + P(1) + P(2) + P(3) + P(4) + P(5)).
The last argument "1" of the function means "the cumulative mode".
Solved.
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