Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.

A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.223, 0.335, 0.251, 0.126, and 0.047, respectively.

Thank you for the opportunity to help you with your question!

Hi, Elsa! So this is NOT a probability distribution. The reason why it is not a probability distribution is because all values reported in a given day must equal 1. .223+.335+.251+..126+.047 = .982. So, this is is less than 1 and does not equal 1.

In order to satisfy requirement for probability distribution, we need to add a car theft that would equal to 1. Since we don't know what the exact probability of 5 car thefts are, we must add X>4= probability of .018 . Adding the probability of .018 brings the probability up to 1 which would satisfy the requirement.

Please let me know if you need any clarification. I'm always happy to answer your questions.