Question

1. A certain highway has an average of 4 car accidents each week.

(a) What is the probability that at least one accident occurs this week?

(b) What is the probability that exactly 7 accidents occur during the next two weeks?

(c) What is the probability that at least one accident occurs tomorrow?

Answer 1

a)

X ~ Poisson ()

P(X) = e^-X / X!

a)

P( X >= 1) = 1 - P( X = 0)

= 1 - e^-4

= 0.9817

b)

For 2 weeks, = 2 * 4 = 8

P( X = 7) = e^-8 * 8⁷ / 7!

= 0.1396

c)

For a day, = 4/7

P(X >= 1) = 1 - P( X = 0)

= 1 - e^-4/7

= 0.4353