Find an example from either the news, your research, or your day-to-day life where someone has confused the conditional probability for either the probability of an event or the probability of an intersection. Respond to another student’s example and describe how the reported probability may change if the conditional probability was correctly considered.

Student#1 initial post;

One example I can think of in which the probability of an event was confused with conditional probability in my day-to-day life involved a situation with a close family member who misunderstood their physician's warning regarding their risk of developing a rare form of cancer. Quick note: I was permitted by the individual involved to discuss this story with the class. In 2018 this individual was notified by their physician that they tested positive for the RET Proto-Oncogene, the gene thought to be responsible for the development of a rare hereditary cancer known as MEN2A or Multiple Endocrine Neoplasia Type Two Medullary Thyroid Carcinoma. They were then notified that it would be in their best interest for their health to have their thyroid removed to limit the possible development ad spread of the disease. They decided against the proposed surgery after doing some online research. They found that Medullary Thyroid Carcinoma only makes up 2-4% of individuals diagnosed with thyroid cancer and has a diagnosis rate of approximately 1,000 people per year in the United States (probability of the event) (Cleveland Clinic, n.d). They failed to consider their positive RET Proto-Oncogene test result at the time of their research, which is believed to increase one's probability of developing MEN2A to 90% (Cleveland Clinic, n.d). As conditional probability refers to the chance of some outcome occurring given that another event has also occurred, the conditional probability of my family friend developing hereditary MEN2A Medullary Thyroid Carcinoma depended on them being a carrier of the RET Proto-Oncogene. The family friend was diagnosed with MEN2A but has been fortunate enough to be in remission.

References

Cleveland Clinic. (n.d.). *Medullary thyroid cancer (MTC): Symptoms & treatment*. Retrieved from

Student Initial post#2

I could not think of any example from my research or from the news where someone has confused the conditional probability for either the probability of an event or the probability of an intersection. However, I recently discussed with my friends what percentage of rain on the iPhone weather app really means. If the weather forecast calls for 60% chance of rain, I never knew how to correctly interpret that number. After doing some research, I realized that the internet and professionals are not in agreement either on what it means and how it is calculated. Percent rain or referred to by meteorologists as the Probability of Precipitation (PoP) does not attempt to predict how likely rain is to occur but rather is the “statistical probability that a given point in a forecast area will receive at least 0.01 inches of precipitation in the specified time period.” In other words, the rain percentage on your weather app refers to the chance you will experience a measurable amount of precipitation (0.01”) in the given period. The calculation depends on the **confidence** a forecaster has that rain will occur and on how widespread it is expected to be ( **area affected**).

Anyway, I thought it was a good example to see how a probability can depend on previous events and we can end up with the same percent chance but get there with different probabilities for an event. Here is an example:

If the forecaster is 100% confident that 30% of the Valley will get rainfall, then there’s a 30% chance for rain.

If the forecaster is 50% confident that 60% of the Valley will get rainfall, then there’s a 30% chance for rain AS WELL!