Question 61249: A statistics student needs a grade of at least 70 to pass an examination. The exam consists of 10 true/false questions. If he guesses at each question, what is the probability he will pass? and if the test was changed to 10 multiple-choice questions having 5 possible answers to choose from and he is still guessing what is the probability he will pass?
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! I hope you're allowed to use a TI-83 or 84 for this, otherwise, it's kind of a pain!
A statistics student needs a grade of at least 70 to pass an examination. The exam consists of 10 true/false questions. If he guesses at each question, what is the probability he will pass? and if the test was changed to 10 multiple-choice questions having 5 possible answers to choose from and he is still guessing what is the probability he will pass?
:
This is a binomial probability problem.
n=10 (The number of questions)
p=.5 (1/2 chance of getting a true-false question right)
q=1-.5=.5 (1/2 chance of getting it wrong)
x=7,8,9,10 (because he can pass with a 70,80,90, or 100)
:
The formula is:
P(x)=probability of x
n=number of trials
x=number of successes
p=probabillty of success
q=1-p=probabilty of failure
:
Add all the probability of x=7,8,9,10 together and the students has a probability of .171875 of passing. If you have a TI-83/84
1-binomialcdf(10,.5,6)=.171875
:
For the second one, everything is the same except:
p=1/5=.2 and q=4/5=.8
Add the probabilities of x=7,8,9,10 together and the student has a .0008643584 chance of passing.
1-binomialcdf(10,.2,6)=8.643584E-4=.0008643584
:
If I were the student, I'd study. Both probabilities are low, and the chance of passing a multiple choice test by guessing is almost 0!
That should be enough to help you solve it. If not, let me know.
Happy Calculating!!!
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