document.write( "Question 1067876: the probability that a student passes a physics test is 2/3. of he takes three physics tests, what is the probability that he passes two of the test? \n" ); document.write( "

Algebra.Com's Answer #683057 by stuylin(8) $\"\"$ $\"About$

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First, we have to know how many cases there are that he passes 2 test, and fails the last test. \r
\n" ); document.write( "\n" ); document.write( "Case 1: pass, pass, fail
\n" ); document.write( "Case 2: pass, fail, pass
\n" ); document.write( "Case 3: fail, pass, pass\r
\n" ); document.write( "\n" ); document.write( "So there are 3 cases. \r
\n" ); document.write( "\n" ); document.write( "Then we have to take into account of the case when he passes all three:\r
\n" ); document.write( "\n" ); document.write( "Case 4: pass, pass, pass\r
\n" ); document.write( "\n" ); document.write( "Now, you replace each of these scenarios with the probability. \r
\n" ); document.write( "\n" ); document.write( "Case 1: (2/3)*(2/3)*(1/3) = 4/27
\n" ); document.write( "Case 2: (2/3)*(1/3)*(2/3) = 4/27
\n" ); document.write( "Case 3: (1/3)*(2/3)*(2/3) = 4/27
\n" ); document.write( "Case 4: (2/3)*(2/3)*(2/3) = 8/27\r
\n" ); document.write( "\n" ); document.write( "Then you add up the probabilities of each of these cases happening:
\n" ); document.write( "(4/27)+(4/27)+(4/27)+(8/27) = 20/27
\n" ); document.write( "Therefore, the probability that he passes two tests is 20/27. \n" ); document.write( "

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