3 Lucy is the captain of her school's cricket team.
The number of catches, \(X\), taken by Lucy during any particular cricket match may be modelled by a Poisson distribution with mean 0.6 . The number of run-outs, \(Y\), effected by Lucy during any particular cricket match may be modelled by a Poisson distribution with mean 0.15 .

1. Find:
   1. \(\mathrm { P } ( X \leqslant 1 )\);
   2. \(\mathrm { P } ( X \leqslant 1\) and \(Y \geqslant 1 )\).
2. State the assumption that you made in answering part (a)(ii).
3. During a particular season, Lucy plays in 16 cricket matches.
   1. Calculate the probability that the number of catches taken by Lucy during this season is exactly 10 .
   2. Determine the probability that the total number of catches taken and run-outs effected by Lucy during this season is at least 15 .