document.write( "Question 741742: A box contains 2 red and 3 green balls.one ball is drawn from the box and replaced before another is drawn.what is the propability that at least one is red? \n" ); document.write( "

Algebra.Com's Answer #852624 by ikleyn(53107) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A box contains 2 red and 3 green balls. One ball is drawn from the box and replaced before another is drawn.
\n" ); document.write( "What is the probability that at least one is red?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The probability that at least one ball of the two is red is the sum\r\n" );
document.write( "\r\n" );
document.write( "    P(1st is red, 2nd is green) + P(1st is green, 2nd is red) + P(both are red).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, calculating this three-terms sum is one approach to solve the problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But there is another approach, more effective and less computationally consuming.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is to calculate the probability \"at least one ball is red\" as the complement to the probability \r\n" );
document.write( "\"both balls are green\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, let calculate the probability that \"both balls are green\".  It is\r\n" );
document.write( "\r\n" );
document.write( "    P(both balls are green) =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, \r\n" );
document.write( "\r\n" );
document.write( "    P(at least one ball is red) = 1 - P(both balls are green) = 1 -  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The probability that at least one ball is red is  .\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" );