Suppose that the average number of cars abandoned weekly on...

Suppose that the average number of cars abandoned weekly on a certain highway is $2.2 .$ Approximate the probability that there will be
(a) no abandoned cars in the next week;
(b) at least 2 abandoned cars in the next week.

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Key Concepts

Probability Mass Function

The probability mass function (PMF) of a Poisson-distributed random variable gives the probability of observing exactly k events. It is expressed as P(X = k) = (e^(-lambda) * lambda^k) / k!, where lambda is the mean rate and k is a non-negative integer. This function is fundamental in calculating the likelihood of specific outcomes for Poisson processes.

Complement Rule

The complement rule in probability is a method used to find the probability of an event by subtracting the probability of its complement from one. In scenarios where it is easier to compute the probability of the event not occurring (or fewer than a desired number of occurrences), this rule simplifies the calculation of the probability of at least or more occurrences.

Poisson Distribution

The Poisson distribution is a discrete probability distribution that models the number of events occurring within a fixed interval of time or space when these events happen with a known constant mean rate and independently of the time since the last event. This distribution is useful for modeling rare events and is characterized by its parameter lambda, which represents the average number of events in the interval.

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