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?
This is a binomial probability problem with
n = 10 independent trials.
p = , the probability of getting 1 answer right in 1 trial.
We want the probability of 6 or more successful (lucky) choices.
We will find the probability of the complement event and subtract
from 1.
The complement event is the event of guessing 5 or fewer answers
correct.
You have a table of cumulative binomial probabilities in the back of your
book, like the one below, for the probabilities of x or fewer successful
choices. Find the one which is headed n=10. Then find
the column headed p = .20 and go down until you are in line with
x = 5 on the far left. There you read 0.994, which I have colored red below.
So your desired probability is gotten by subtracting 1 - 0.994 getting 0.006.
That's the answer 0.006.
n = 10
p .01 .05 .10 .20 .25 .30 .40 .50 .60 .70 .75 .80 .90 .95 .99
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x
0 0.904 0.599 0.349 0.107 0.056 0.028 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.996 0.914 0.736 0.376 0.244 0.149 0.046 0.011 0.002 0.000 0.000 0.000 0.000 0.000 0.000
2 1.000 0.988 0.930 0.678 0.526 0.383 0.167 0.055 0.012 0.002 0.000 0.000 0.000 0.000 0.000
3 1.000 0.999 0.987 0.879 0.776 0.650 0.382 0.172 0.055 0.011 0.004 0.001 0.000 0.000 0.000
4 1.000 1.000 0.998 0.967 0.922 0.850 0.633 0.377 0.166 0.047 0.020 0.006 0.000 0.000 0.000
5 1.000 1.000 1.000 0.994 0.980 0.953 0.834 0.623 0.367 0.150 0.078 0.033 0.002 0.000 0.000
6 1.000 1.000 1.000 0.999 0.996 0.989 0.945 0.828 0.618 0.350 0.224 0.121 0.013 0.001 0.000
7 1.000 1.000 1.000 1.000 1.000 0.998 0.988 0.945 0.833 0.617 0.474 0.322 0.070 0.012 0.000
8 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.989 0.954 0.851 0.756 0.624 0.264 0.086 0.004
9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.972 0.944 0.893 0.651 0.401 0.096
10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
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We can also show you how to find it using your TI-83 or 84 calculator.
It can also be done by formula, although thst would take a lot of
time. I think your teacher intended that you use the binomial tables.
Edwin