A bank offers both adjustable and fixed rate mortgage loans on residential properties, which are classified into three categories:  single-family homes, condominiums, and multi-family homes.  Each loan made in 2010 was classified according to type of mortgage and type of property, as shown in the given table.      Single Family Condo Multi Family   Adjustable 1500 788 337   Fixed Rate 375 377 373                           Answer the following: (Express answers as fractions or to 4 decimal places)       a)  What is the probability that a randomly chosen loan was for a condo?       b)  What is the probability that a randomly chosen loan was for a fixed rate, given that is was on a single family home?      c)  What is the probability that a randomly chosen loan was for a multi family home, given that it was an adjustable rate loan?

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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.