On average, 3 traffic accidents per month occur at a certain...

On average, 3 traffic accidents per month occur at a certain intersection. What is the probability that in any given month at this intersection
(a) exactly 5 accidents will occur?
(b) fewer than 3 accidents will occur?
(c) at least 2 accidents will occur?

Key Concepts

Cumulative Probability

Cumulative probability refers to the sum of probabilities for a range of outcomes. In the context of the Poisson distribution, it is used to determine the probability of observing up to a certain number of events, such as fewer than a specified number.

Complement Rule

The complement rule is a probability technique used to calculate the probability of an event by subtracting the probability of the event’s complement from one. This is particularly useful for events defined by 'at least' or 'more than' criteria, where direct calculation may be complex.

Poisson Probability Mass Function (PMF)

The Poisson PMF is the mathematical formula used to calculate the probability of exactly k events occurring in a fixed interval. The formula is P(X = k) = (?^k e^(-?)) / k!, which provides a direct method to evaluate specific event counts.

Poisson Distribution

The Poisson distribution is a probability distribution that describes the likelihood of a given number of events occurring in a fixed interval of time or space, given the events occur with a known constant mean rate and independently of the time since the last event.

Mean Rate (?)

The mean rate, denoted as ?, represents the average number of events (such as accidents) expected in a given interval. It is a key parameter in the Poisson distribution that influences the shape of the probability distribution.

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