CAIE S2 Specimen — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
SessionSpecimen
TopicPoisson Distribution
TypeTwo independent Poisson sums

1 Failures of two computers occur at random and independently. On average the first computer fails 1.2 times per year and the second computer fails 2.3 times per year. Find the probability that the total number of failures by the two computers in a 6-month period is more than 1 and less than 4 .