Question

If a probability that A,B and C will solve a problem is 1/2,3/4 and2/3.what is the probability that the problem will be solved

Answer 1

Find the probability Q that the problem will not be solved:

$Q = (1 - p(A))(1 - p(B))(1 - p(C)) = \left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{3}{4}} \right)\left( {1 - \frac{2}{3}} \right) = \frac{1}{{24}}$

Then the wanted probability, as the probability of the opposite event, is

$P = 1 - Q = 1 - \frac{1}{{24}} = \frac{{23}}{{24}}$

Answer: 23/24