Question

The probability of a car having a flat tire while driving on a Bridge is 0.00005. If 10,000 cars cross the bridge each day, what is the probability that at most 2 cars will have a flat on the bridge. (Hint, the average is 0.5 flat tires/day/car).

Answer 1

X ~ Poisson ($\lambda$​​​​​​)

Where $\lambda$ = 0.00005 * 10000 = 0.5

Poisson probability distribution is

P(X) = e^-$\lambda$$\lambda$^X / X!

P( X <= 2) = P (X = 0) + P( X = 1 ) + P( X = 2)

= e^-0.5 + e^-0.5 * 0.5 + e^-0.5 * 0.5² / 2!

= 0.9856