# 1 - Probability for cars to pass through a point on road in a 5-minute period

**Problem**

The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (*a*) two cars go past and (*b*) fewer than 3 cars go past.

**Solution**

$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$

$P(2) = \dfrac{e^{-4} (4^2)}{2!} = 0.146$
$\displaystyle P(\lt 3) = \sum_{x = 0}^2 \dfrac{e^{-4} (4^x)}{x!} = 0.238$

Part (*a*)

Part (*b*)

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