document.write( "Question 346244: 2. A machine has twelve identical components that function independently. It will stop working if three or more of the components fail. If the probability that an individual component fails is 0.11, find the probability that the machine will be working. \n" ); document.write( "

Algebra.Com's Answer #247601 by Fombitz(32388) $\"\"$ $\"About$

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Look at the probability of $\"0\"$ , $\"1\"$ , and $\"2\"$ components failing.
\n" ); document.write( " $\"0\"$ failures: $\"P%280%29=1%2A%280.89%29%5E12%2A%280.11%29%5E0=0.24699\"$
\n" ); document.write( " $\"1\"$ failure: $\"P%281%29=12%2A%280.89%29%5E11%2A%280.11%29%5E1=0.36632\"$
\n" ); document.write( " $\"2\"$ failures: $\"P%282%29=66%2A%280.89%29%5E10%2A%280.11%29%5E2=0.24902\"$
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\n" ); document.write( "P(working)= $\"P%280%29%2BP%281%29%2BP%282%29=0.86233\"$
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\n" ); document.write( "The coefficients are generated by $\"a%5Bn%2Cr%5D=%28matrix%282%2C1%2Cn%2Cr%29%29\"$ which are the first 3 Pascal triangle coefficients for ( $\"12%2B1\"$ ) $\"13\"$ terms.
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