document.write( "Question 623743: The Odds against A solving a problem in statistics are 10 to 8; the odds in favour of B and C solving the same problem 12 to 9 and 15 to 10 respectively. What are the probabilities that the problem will be solved and all three will solve the problem \n" ); document.write( "

Algebra.Com's Answer #392379 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
the following reference tells you how to convert from odds to probabilities and vice versa.
\n" ); document.write( "http://www.math-magic.com/probability/prob_to_odds.htm
\n" ); document.write( "application of the rules in your problem yield the following:
\n" ); document.write( "The Odds against A solving a problem in statistics are 10 to 8; the odds in favour of B and C solving the same problem 12 to 9 and 15 to 10 respectively. What are the probabilities that the problem will be solved and all three will solve the problem.
\n" ); document.write( "Probability of A not solving the problem is 10 / 18, therefore:
\n" ); document.write( "Probability of A solving the problem is 8/18.
\n" ); document.write( "Probability of B solving the problem is 12/21.
\n" ); document.write( "Probability of C solving the problem is 15/25.
\n" ); document.write( "Since solving the problem by either A, or B, or C are independent events (they are not collaborating with each other), then the probability that A or B or C will solve the problem is equal to 8/18 + 12/21 + 12/25.
\n" ); document.write( "This winds up as the probability that the problem will be solved since only A or B or C are trying to solve the problem.
\n" ); document.write( "The probability that A and B and C will all 3 solve the problem is equal to 8/18 * 12/21 * 12/25.
\n" ); document.write( " \n" ); document.write( "

\n" );