Binomial with derived parameters

Questions where n or p must be derived from given information (e.g., 'average number of 5s was 4.8' to find p, or 'mean number of defectives is 1.6' in packs of 20) before calculating probabilities.

2 questions

CAIE S1 2011 June Q1

1 A biased die was thrown 20 times and the number of 5 s was noted. This experiment was repeated many times and the average number of 5 s was found to be 4.8 . Find the probability that in the next 20 throws the number of 5 s will be less than three.

CAIE S1 2009 November Q1

1 The mean number of defective batteries in packs of 20 is 1.6 . Use a binomial distribution to calculate the probability that a randomly chosen pack of 20 will have more than 2 defective batteries.