Question

question 5: on a given day, there is a car accident reported at the intersection of victory blvd and richmond avenue with a probability 0.05. what is the probability that there are at most 2 car accidents reported thoughout a month?

Answer 1

To find the probability of at most 2 car accidents reported throughout a month, calculate the probabilities of 0, 1, and 2 accidents using the Poisson distribution with an average of 0.05 accidents per day. Sum up these probabilities to get the answer.

Step-by-step explanation:

To find the probability that there are at most 2 car accidents reported throughout a month, we need to calculate the probability of 0, 1, and 2 accidents.

1. To calculate the probability of 0 accidents, we use the Poisson distribution with an average of 0.05 accidents per day and multiply it by the number of days in a month (30): P(0 accidents) = (e^(-0.05) * 0.05^0) / 0! * 30
2. To calculate the probability of 1 accident, we use the same formula but replace the average with 0.05 and the exponent with 1: P(1 accident) = (e^(-0.05) * 0.05^1) / 1! * 30
3. To calculate the probability of 2 accidents, we replace the exponent with 2: P(2 accidents) = (e^(-0.05) * 0.05^2) / 2! * 30

Finally, we sum up the probabilities of 0, 1, and 2 accidents to get the probability of at most 2 accidents.

Answer 2

The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.