Accidents at two factories occur randomly and independently. On average, the numbers of accidents per month are $$$3.1$$$ at factory $$$A$$$ and $$$1.7$$$ at factory $$$B$$$. Find the probability that the total number of accidents in the two factories during a 2-month period is more than 3. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_61 Year：2021 Question No：1

Answer:

$\lambda=(3.1+1.7) \times 2$
$=9.6$
$1-\mathrm{e}^{-9.6}\left(1+9.6+\frac{9.6^{2}}{2}+\frac{9.6^{3}}{3 !}\right)$
$=0.986(3 \mathrm{sf})$

6.1.1 use formulae to calculate probabilities for the distribution $\text { Po }(\lambda)$

6.2.1.6 if and have independent Poisson distributions then X + Y has a Poisson distribution. (Proofs of these results are not required.)