4. A bag contains 40 beads of the same shape and size. The ratio of red to green to blue beads is \(1 : 3 : 4\) and there are no beads of any other colour. In an experiment, a bead is picked at random, its colour noted and the bead replaced in the bag. This is done ten times.

1. Suggest a suitable distribution for modelling the number of times a blue bead is picked out and give the value of any parameters needed.
2. Explain why this distribution would not be suitable if the beads were not replaced in the bag.
3. Find the probability that of the ten beads picked out
   1. five are blue,
   2. at least one is red. The experiment is repeated, but this time a bead is picked out and replaced \(n\) times.
4. Find in the form \(a ^ { n } < b\), where \(a\) and \(b\) are exact fractions, the condition which \(n\) must satisfy in order to have at least a \(99 \%\) chance of picking out at least one red bead.