Question

Based on this data set, are the events that the randomly selected first-major-hurricane-of-season is located on the Atlantic and the event that the selected first-major-hurricane-of-season is in July independent events? On your "scratch paper" use a calculation and explanation to justify the answer you chose. ta on Month of First Hurricane of

Season Water Jun Jul Aug Sep Summary

Atlantic (A) 0 0 6 2 8

Both (B) 0 1 0 0 1

Gulf (G) 2 2 0 0 4

Summary 2 3 6 2 13

Answer 1

Let

• A=event that the randomly selected first-major-hurricane-of-season is located on the Atlantic
• July=the event that the selected first-major-hurricane-of-season is in July

We can find the following probabilities

The joint probability that a randomly selected first-major-hurricane-of-season is located on the Atlantic and the selected first-major-hurricane-of-season is in July is

The marginal probability that a randomly selected first-major-hurricane-of-season is located on the Atlantic is

The marginal probability that a randomly selected first-major-hurricane-of-season is in July is

2 events are independent if the joint probability of the 2 events is equal to the product of marginal probabilities, that is

Here the product of marginal probabilities is

This is not equal to the joint probability

Hence, we can say that the events that the randomly selected first-major-hurricane-of-season is located on the Atlantic and the event that the selected first-major-hurricane-of-season is in July are not independent events.

ans: No