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

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) (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) (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.

RELATED QUESTIONS
The odds against students X solving a statistics problem are 8:6 and odds in favor of a (answered by stanbon)
(a) A problem in business statistics is given to five students A,B,C,D and E. Their... (answered by Emsley)
The Raptors have an 80% chance of winning the next playoffs. a.What are the odds in... (answered by ikleyn)
b) The odds against student X solving a Business statistics problem are 8 to 6, and odds... (answered by stanbon)
Tomarrow is my unversity paper please give me ans fast as much as possible The odds... (answered by oscargut)
Teaghan plays basketball. She scored 18 of her 20 last free throws. ___ A) What are... (answered by jorel1380)
Find the probability whose odds against are given in the problem. Odds against are 10000 (answered by solver91311)
find the probability whose odds against are given in the problem odds against are 5... (answered by stanbon)
If the odds in favor of your winning a bet are 3 to 8, what are the odds against winning... (answered by Fombitz)