SOLUTION: A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering
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Question 438940: A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering less than 2 questions correctly.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by !})
The probability of less than 2 is the probability of zero plus the probability of one, so:
\ =\ P_6(0,0.25)\ +\ P_6(1,0.25)\ =\ \left(6\cr 0\right\)\left(0.25\right)^0\left(0.75\right)^{6}\ +\ \left(6\cr 1\right\)\left(0.25\right)^1\left(0.75\right)^{5})
6 taken zero at a time is 1 and 6 taken 1 at a time is 6. Anything to the zero power is 1, anything to the 1 power is itself. You can do the rest of the arithmetic. The answer is slightly more than 50%.
John
My calculator said it, I believe it, that settles it
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