A bag contains a large number of counters of which \(15 \%\) are coloured red. A random sample of 30 counters is selected and the number of red counters is recorded.
Find the probability of no more than 6 red counters in this sample.
A second random sample of 30 counters is selected and the number of red counters is recorded.
Using a Poisson approximation, estimate the probability that the total number of red counters in the combined sample of size 60 is less than 13.