SOLUTION: find the probabiliy that the problem will be solved of the probability of a, b, c solving a problem is 1/3, 2/7 & 3/8 respectivly. if the three try to solve the problem simultaneou

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Question 1038861: find the probabiliy that the problem will be solved of the probability of a, b, c solving a problem is 1/3, 2/7 & 3/8 respectivly. if the three try to solve the problem simultaneously.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the probability of a solving the problem is 1/3.
the probability of b solving the problem is 2/7.
the probability of c solving the problem is 3/8.

i'm not totally sure, but i think this problem falls under the following rule.

p(a or b or c) = p(a) + p(b) + p(c) - p(ab) - p(ac) - p(bc) + p(abc).

a good reference on this can be found here:

http://statistics.about.com/od/Formulas/a/Probability-Of-The-Union-Of-Three-Or-More-Sets.htm

assuming that a and b and c are working independently of each other, then ....

p(ab) = 1/3 * 2/7.
p(ac) = 1/3 * 3/8.
p(bc) = 2/7 * 3/8.
p(abc) = 1/3 * 2/7 * 3/8

p(ab) measn that a and b solve the problem at the same time.
likewise for p(ac) and p(bc).
p(abc) means that all 3 solve the problem at the same time.

your answer should be:

p(a or b or c) = p(a) + p(b) + p(c) - p(ab) - p(ac) - p(bc) + p(abc) which becomes:

p(a or b or c) = 1/3 + 2/7 + 3/8 - (1/3 * 2/7) - (1/3 * 3/8) - (2/7 * 3/8) + (1/3 * 2/7 * 3/8)