CAIE S2 2024 June — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2024
SessionJune
TopicPoisson Distribution
TypeThree or more independent Poisson sums

1 A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10 -second period have the independent distributions \(\operatorname { Po } ( 0.4 ) , \operatorname { Po } ( 0.1 ) , \operatorname { Po } ( 0.2 )\) and \(\mathrm { Po } ( 0.5 )\). Find the probability that the total number of passengers arriving at the four entrances to the bus station during a randomly chosen 1 -minute period in the morning is more than 3 .