The probability of exactly three accidents at a traffic intersection in any given year is calculated using the Poisson distribution, which describes the probability of a certain number of occurrences over a certain amount of time. The formula for this calculation is P(x) = (e^-μ)(μ^x)/ x!, where x is the desired number of occurrences (in this case, 3), e is Euler’s constant (2.71828…), and μ represents the average number of yearly accidents at that same intersection (5). Plugging these values into the equation gives us: P(3) = (.0067)(125)/6 = .1389, or 13.89%.
The average number of yearly accident at a traffic intersection is 5. Find the probability that there are exactly three accidents at the same intersection this year.
This means that there is a 13.89% chance that there will be exactly three accidents at this particular traffic intersection this year. While this may seem like quite a low figure, it should be noted that it still represents a relatively high probability compared to other events occurring on any given day—for instance, it would take much more than 13.89% odds to win an individual lottery ticket drawing.
Therefore, while not incredibly likely to occur, there is certainly still some risk associated with driving through intersections with known histories of multiple past collisions; drivers should exercise extra caution when navigating such areas and always drive responsibly as they get around town.