SOLUTION: A test consists of 10 true and false questions. To pass the test a student must answer at least 9 questions correctly. If the student guesses on each questions what is the probabil
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Question 1113461: A test consists of 10 true and false questions. To pass the test a student must answer at least 9 questions correctly. If the student guesses on each questions what is the probability that the student will pass the test?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where the probability of success on any given trial is 
is given by:
\ =\ {{n}\choose{k}}\,\cdot\,\(p\)^k\,\cdot\,\(1\,-\,p\)^{n\,-\,k})
Where 
is the number of ways to choose things from things calculated by !})
.
To answer the given question you need to calculate the probability of getting exactly 9 out of 10 questions correct and the probability of getting all 10 out of 10 questions correct when the probability of getting any single question correct is 0.50 and then find the sum of those two probabilities.
\ =\ {{10}\choose{9}}\,\cdot\,\(.5\)^9\,\cdot\,\(1\,-\,0.5\)^{10\,-\,9}\ +\ {{10}\choose{10}}\,\cdot\,\(.5\)^{10}\,\cdot\,\(1\,-\,0.5\)^{10\,-\,10})
A couple of facts that will make the arithmetic simpler:
John
My calculator said it, I believe it, that settles it
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