1.  

sample space

2.

(2.7)

3.

(0.4)(0.2)(0.5) / 0.292

4.

(0.5)(0.6) + (0.3)(0.3) + (0.2)(0.8)

5.

Denominator is as in #4.  Numerators for the three times are (0.5)(0.6),
(0.3)(0.3) and (0.2)(0.8), of which 9:00 is the largest.  The requested
probability is then 

(0.5)(0.6) / [(0.5)(0.6) + (0.3)(0.3) + (0.2)(0.8)]