1).  1/2

         2).  1/4

         3).  1/8

    Notes
  Suppose x, y, z stand for the decimal parts of c, g, s
  respectively. We may assume that each of x, y, z, is
  distributed uniformly between 0 and 1.  

  1). x must lie between 0.25 and 0.75, so probability = 1/2.

  2). The condition is satisfied if:
       (i) neither c nor g is rounded up, but (c+g) is rounded  
        up, i.e. x < 0.5, y < 0.5, x+y > 0.5
    or (ii) both c and g are rounded up, but (c+g) is not
        doubly rounded up,
        i.e. x > 0.5, y > 0.5, x+y < 1.5



  The coloured areas on the diagram show the values of x and y
   which satisfy these conditions. Total = 1/8 + 1/8 = 1/4. 

  3). The condition is satisfied only if c, g, s are all
       rounded up, i.e. x > 0.5, y > 0.5, z > 0.5.
      But x, y, x are not independent. In fact x+y+z must = 2.
      So taking x and y as the independent variables, we
       require:  x > 0.5, y > 0.5, 2-x-y > 0.5.
      This corresponds to the red area in the diagram,
       whose area is 1/8.

  1. The hot tap alone could fill a bath in 6 minutes, and the
      cold tap alone could fill it in 3 minutes. How long will
      it take to fill the bath with both taps running?

  2. Water from the hot tap is at 75 degrees C, and from the
      cold tap is at 15 degrees C. If the bath is filled with
      both taps, as in question 1, what will be the temperature
      of the bath water? 

  3. A dishonest innkeeper has a litre bottle full of whisky.
      Each time he serves a measure of whisky he dispenses 5 cl,
      but then secretly fills up the bottle with water. How many
      times can he do this before the whisky becomes half strength?