“Why does it have to be me?” This is likely the first question that one would ask when faced with an unfortunate diagnosis, such as a heart disease. This week, we take a mathematical view of this question.
On hearing about the disease — let us call it X, most patients would search for details on the internet. Google might instantly tell us that X only affects 5% of people, which means one in 20 people. This statistic further increases the anxiety; why should I be in the 5% and not in the 95%. It indeed seems surprising to be subject to such a low chance event, isn’t it? Yet, a lot of people, much more than 5%, find themselves asking this question.
To understand it mathematically, we need to consider all possibilities, even diseases other than X. If our patient were to be diagnosed with another 5% disease such as a liver disease, Y, would he not have asked the same “why me”? Assuming X and Y are unrelated, let us consider the various possibilities in a city of 100 people. The first possibility is that of being affected by X but not Y. The chance of this is 95% of 5% of 100, which is 4.75. The same calculation applies for those who catch Y but not X. The unfortunate occurrence of being diagnosed with both happens in 5% of 5% cases, which is in 0.25. Now, the least worrying scenario, that of being free of both X and Y. This is 95% of 95%, which is 90.25.
Event - Chance
X but not Y - 4.75
Y but not X - 4.75
Neither X nor Y - 90.25
X and Y - 0.25
Now, sit back and look at this table again. Only 90.25% people are free of both diseases, 9.75% have at least one of X or Y. This is when it gets really interesting. While 9.75% of people, not 5%, would catch either X or Y; each of them will look up Google and ask “why am I in the 5%?”
There is no stopping there, X and Y are not the only rare diseases. There are many. Considering five rare diseases, the mathematics works out to suggest that only 77% people would be free from all of them!
(Dr Deepak P. is a computer scientist and academic staff at Queen's University Belfast, UK)
