document.write( "Question 575605: you flip three coins. What is the probabilty that you get at least two heads, fiven that you get at least one head? \n" ); document.write( "

Algebra.Com's Answer #369554 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
This one can be tricky (read about the \"Boy or Girl paradox\" http://en.wikipedia.org/wiki/Boy_or_Girl_paradox) because it does not specify which coin is a head, just that at least one is a head. I would probably list all of the possibilities in our sample space:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "HHH
\n" ); document.write( "HHT
\n" ); document.write( "HTH
\n" ); document.write( "THH
\n" ); document.write( "HTT
\n" ); document.write( "THT
\n" ); document.write( "TTH\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(TTT cannot be in our sample space). Therefore there are seven possibilities, and four of them have at least two heads. The probability is 4/7.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This is similar to the Boy or Girl paradox, which states that a mother has two children; at least one of them is a boy. Surprisingly, the probability that both children are boys is 1/3, not 1/2. However, if you stated something comparative, such as \"the older child is a boy\" then the probability would be 1/2. \n" ); document.write( "

\n" );