Standard +0.3 This question requires knowing that independent Poisson distributions sum to another Poisson (Po(0.4)+Po(0.1)+Po(0.2)+Po(0.5)=Po(1.2)), scaling the rate for 60 seconds (Po(7.2)), and calculating P(X>3)=1-P(X≤3) using tables. It's a straightforward application of standard Poisson properties with minimal problem-solving, making it slightly easier than average.
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 .
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 .\\
\hfill \mbox{\textit{CAIE S2 2024 Q1 [3]}}