document.write( "Question 1201802: A box of 30 flashbulbs contains 3 defective . A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in the sample. (A) Find the probability distribution of X. \n" ); document.write( "

Algebra.Com's Answer #836315 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A box of 30 flashbulbs contains 3 defective . A random sample of 2 is selected and tested.
\n" ); document.write( "Let X be the random variable associated with the number of defective bulbs in the sample.
\n" ); document.write( "(A) Find the probability distribution of X.
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        As this problem is worded, it tells me that it assigned to a person
\n" ); document.write( "        who has some necessary prerequisites and understand simple separated cases.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        So I will not go in detailed explanations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The random variable X may have one of three values: X= 0, 1, 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "P(X=0) is the probability that a random sample of 2 flashbulbs contains 0 defective.\r\n" );
document.write( "\r\n" );
document.write( "The probability for it is  P(X=0) =  =  =  = 0.806896552 (rounded).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "P(X=1) is the probability that a random sample of 2 flashbulbs contains 1 defective.\r\n" );
document.write( "\r\n" );
document.write( "The probability for it is  P(X=1) =  =  =  = 0.186206897 (rounded).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "P(X=2) is the complement of P(X=0) + P(X=1) to 1, so we calculate it this way \r\n" );
document.write( "\r\n" );
document.write( "    P(X=2) = 1 - 0.806896552 - 0.186206897 = 0.006896551.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can check the value P(X=2) this way  P(X=2) =  =  = .  117+27+1 = 145.  ! correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );