Calculating Probability for Vehicle Traffic at a Dual Carriageway Junction

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In summary, the conversation discusses the calculation of probabilities for a Poisson distribution where the mean is 1.6 vehicles per minute passing through a specific junction. The probability of no vehicles passing in a one minute period is 1, the probability of more than 6 vehicles passing in a one minute period is 0, and the probability of fewer than 3 vehicles passing in a five minute period is 0.
  • #1
amcsquared
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Can someone help me out with this? (its not for school)

During the night the number of vehicles passing a particular junction on a dual carriageway follows a Poisson distribution with a mean of 1.6 vehicles per minute. Calculate the probability:
(i) That in a one minute period no vehicles pass the junction. (1)
(ii) That in a one minute period more than 6 vehicles pass the junction. (2)
(iii) That in a five minute period fewer than 3 vehicles pass the junction. (3)
 
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  • #2
Well, do you know what the probability density function for a Poisson distribution looks like? Do you know what the values of that function represent?
 
  • #3
Even if this question really is not for school, it still belongs in a homework forum. (I moved it)
 

FAQ: Calculating Probability for Vehicle Traffic at a Dual Carriageway Junction

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is typically expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

How is probability calculated?

There are different ways to calculate probability depending on the type of event. For simple events, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For more complex events, probability can be calculated using mathematical formulas or statistical methods.

What is the difference between theoretical and empirical probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Empirical probability is based on actual observations or data and takes into account the frequency of each outcome. In general, theoretical probability is used in theoretical scenarios, while empirical probability is used in real-world situations.

What is the law of large numbers?

The law of large numbers states that as the number of trials or experiments increases, the observed results will tend to approach the theoretical probability. In other words, the more times an event is repeated, the closer the actual results will be to the expected results.

How is probability used in real life?

Probability is used in many real-life applications, including weather forecasting, insurance, stock market analysis, and games of chance. It can also be used in decision-making and risk assessment to evaluate the likelihood of certain outcomes.

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