document.write( "Question 61048: on a true/false test a student has no idea what the answers are to 3 of the questions so he guesses. What is the probability that he will guess correctly on all 3 questions? at least 2 times? \n" ); document.write( "
Algebra.Com's Answer #41969 by funmath(2933)\"\" \"About 
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on a true/false test a student has no idea what the answers are to 3 of the questions so he guesses. What is the probability that he will guess correctly on all 3 questions? at least 2 times?
\n" ); document.write( "There's 1 write answer out of two choices for each question. Therefore there's a \"%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29=1%2F8\" probability of guessing all three questions right.
\n" ); document.write( "Percetagewise that's 12.5%. Note that that's the same probability of getting them all wrong (think about it.).
\n" ); document.write( "At least two right is 2 out of three and 3 out of three
\n" ); document.write( "There are three ways to get 2 right (wrr),(rwr),(wrr) and one way to get them all right (rrr)
\n" ); document.write( "\"%281%2F2%29%281%2F2%29%281%2F2%29\"+\"%281%2F2%29%281%2F2%29%281%2F2%29\"+\"%281%2F2%29%281%2F2%29%281%2F2%29\"
\n" ); document.write( "\"1%2F8%2B1%2F8%2B1%2F8=3%2F8\" ways to get 2 right
\n" ); document.write( "\"%281%2F2%29%281%2F2%29%281%2F2%29=1%2F8\" ways to get 3 right
\n" ); document.write( "\"3%2F8%2B1%2F8=4%2F8=1%2F2\" ways to get 2 or 3 right. Note that this is the same probability of getting less than 2 right. (think about it.)
\n" ); document.write( "You can use binomial probability for this, but it would only be easier to do for a problem this small if you have a capable calculator. If you have a TI-83 or 84. Just hit, binomialpdf(3,.5,2)+binomialpdf(3,.5,3)=.5 or 1/2.
\n" ); document.write( ":
\n" ); document.write( "The formula for binomial probability is:
\n" ); document.write( "\"highlight%28P%28x%29=%28n%21%2F%28%28n-x%29%21%2Ax%21%29%29%2Ap%5Ex%2Aq%5E%28n-x%29%29\"
\n" ); document.write( "P(x)=probability of x
\n" ); document.write( "n=number of trials
\n" ); document.write( "x=number of successes
\n" ); document.write( "p=probabillty of success
\n" ); document.write( "q=1-p=probabilty of failure
\n" ); document.write( "For the probability of 2 correct answers:
\n" ); document.write( "n=3, x=2, p=1/2=.5, q=1-1/2=.5
\n" ); document.write( "For the probabilty of 3 correct answers:
\n" ); document.write( "n=3, x=3, p=.5, q=.5
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\n" ); document.write( "\"P%28x%3E=2%29=%283%2F1%29%2A.5%5E2%2A.5%2B%281%29%2A.5%5E3\"
\n" ); document.write( "\"P%28x%3E=2%29=%283%2F1%29%2A.5%5E2%2A.5%2B%281%29%2A.5%5E3\"
\n" ); document.write( "\"P%28x%3E=2%29=3%2A.5%5E2%2A.5%2B.5%5E3\"
\n" ); document.write( "\"P%28x%3E=2%29=3%2A.5%5E2%2A.5%2B.5%5E3\"
\n" ); document.write( "\"P%28x%3E=2%29=3%28.25%29.5%2B.125\"
\n" ); document.write( "\"P%28x%3E=2%29=3%28.125%29%2B.125\"
\n" ); document.write( "\"P%28x%3E=2%29=.375%2B.125\"
\n" ); document.write( "\"highlight%28P%28x%3E=2%29=.5%29\"
\n" ); document.write( "Happy Calculating!!!
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