Successful completion of a construction project depends on the supply of materials and labor as well as the weather condition. Consider a given project that can be successfully completed if either one of the following conditions prevails: (i) Good weather and at least labor or materials are adequately available, (ii) Bad weather but both labor and materials are adequately available. Define: G = Good weather G' = Bad weather L = Adequate labor supply M = Adequate materials supply C = Successful completion Suppose P(L) = 0.7; P(G) = 0.6 and L is independent of both M and G. If the weather is good,adequate supply of materials is guaranteed, whereas the probability of adequate supply of material is only 50% if bad weather prevails. Formulate the event of successful completion in terms of G, L, and M. Determine the probability of successful completion. If the project was successfully completed, what is the probability that labor supply had been inadequate?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.