suppose that on a given weekend the number of accidents at a certain inter- section follows a poisson distribution with mean 0.7. what is the probability that at least three accidents occur during the weekend?



Answer :

0.0341 is the probability that at least three accidents occur during the weekend

What is probability distribution?

A probability distribution is the mathematical function that provides the odds of occurrence of many possible outcomes for an experiment in probability theory and statistics.

What is Poisson distribution?

A discrete probability distribution is a Poisson distribution. It provides the likelihood that an event will occur a specific number of times (k) over a predetermined period of time or area. The mean number of occurrences (lambda), which is the sole parameter of the Poisson distribution, is a function.

Poisson distribution :

P(x accidents) = e^(-0.7) * (0.7)^x / (x!)

P(X>=3)

= 1 - P(x<3)

= 1 - (P(0) + P(1) + P(2))

= 1 - ( [e^(-0.7) * (0.7)^0 / (0!)] + [e^(-0.7) * (0.7)^1 / (1!)] + [e^(-0.7) * (0.7)^2 / (2!)])

= 0.0341

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