Question

Every​ morning, my neighbor goes out walking. I observe that​ 20% of the time she walks with her​ beagle, 70% of the time she walks with her golden​ retriever, and​ 30% of the time she walks alone. If these events are all​ disjoint, is this an example of a valid probability​ distribution?

Answer 1

No, This is not a valid Probability Distribution

Explanation:

Probability [Neighbour walks with Beagle] = 20%

Probability [Neighbour walks with Golden Retriever] = 70%

Probability [Neighbour walks alone] = 30%

Disjoint Events are the events that have zero probability of occurring together. If all the three above items are disjoint, it means that it can never happen that two of them happen together.

The total (summed) probability of a valid probability distribution, with disjoint sets = 1 . In given case, total probability = 0.2 + 0.7 + 0.3 = 1.2 ; i.e > 1.

So, this probability distribution with stated disjoint events is not a Valid Probability distribution.