1 The water in a pond contains three different species of a spherical green algae:
Volvox globator, at an average rate of 4.5 spheres per \(1 \mathrm {~cm} ^ { 3 }\);
Volvox aureus, at an average rate of 2.3 spheres per \(1 \mathrm {~cm} ^ { 3 }\);
Volvox tertius, at an average rate of 1.2 spheres per \(1 \mathrm {~cm} ^ { 3 }\).
Individual Volvox spheres may be considered to occur randomly and independently of all other Volvox spheres. Random samples of water are collected from this pond.
Find the probability that:

1. a \(1 \mathrm {~cm} ^ { 3 }\) sample contains no more than 5 Volvox globator spheres;
2. a \(1 \mathrm {~cm} ^ { 3 }\) sample contains at least 2 Volvox aureus spheres;
3. a \(5 \mathrm {~cm} ^ { 3 }\) sample contains more than 8 but fewer than 12 Volvox tertius spheres;
4. a \(0.1 \mathrm {~cm} ^ { 3 }\) sample contains a total of exactly 2 Volvox spheres;
5. a \(1 \mathrm {~cm} ^ { 3 }\) sample contains at least 1 sphere of each of the three different species of algae.
   [0pt] [3 marks]