Question

Snowfalls occur randomly and independently over the course of winter in a Minesota city. The average is one snowfall every 3 days.

a. What is the probability of five snowfalls in 2 weeks?

b. Find the probability of a snowfall today.

Answer 1

Let $X=$ the number of snowfalls: $X\sim Po(\lambda t).$

a.

$$\lambda t=1\cdot\dfrac{14}{3}=\dfrac{14}{3}$$

$$P(X=5)=\dfrac{e^{-14/3}\cdot(\dfrac{14}{3})^5}{5!}\approx0.1734$$

b.

$$\lambda t=1\cdot\dfrac{1}{3}=\dfrac{1}{3}$$

$$P(X=1)=\dfrac{e^{-1/3}\cdot(\dfrac{1}{3})^1}{1!}\approx0.2388$$