SOLUTION: 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

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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
Found 2 solutions by edjones, Theo:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
8/18 * 12/21 * 15/25
= 4/9 * 4/7 * 3/5
=48/315
=16/105 probability that all three will solve the problem.
.
5/9 * 3/7 * 2/5
30/315
=2/21 probability that no one will solve the problem.
1 - 2/21 = 19/21 probability that the problem will be solved.
.
Ed

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the following reference tells you how to convert from odds to probabilities and vice versa.
http://www.math-magic.com/probability/prob_to_odds.htm
application of the rules in your problem yield the following:
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.
Probability of A not solving the problem is 10 / 18, therefore:
Probability of A solving the problem is 8/18.
Probability of B solving the problem is 12/21.
Probability of C solving the problem is 15/25.
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.
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.
The probability that A and B and C will all 3 solve the problem is equal to 8/18 * 12/21 * 12/25.