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Latin American Leaders and Cancer: A Probability Analysis

14 Mar

Latin American Leaders and Cancer: A Probability Analysis

Richard Charnin

Mar. 14, 2013

Hugo Chavez was one of seven (six leftist) Latin-American leaders recently diagnosed with cancer. Columbia’s conservative President Juan Manuel Santos was struck with prostate cancer after beginning peace talks with left wing FARC. The six leftists: Brazilian President Dilma Rousseff, Paraguay’s Fernando Lugo, former Brazilian leader Luiz Inácio Lula da Silva, Argentina’s former President Nestor Kirchner. Argentina’s current President Cristina Fernández de Kirchner was diagnosed with thyroid cancer in December 2012, although later analysis proved she had never actually suffered from the illness. In 2006, it was reported that retired Cuban leader Fidel Castro was also diagnosed with cancer, so there were at least EIGHT in total.

To estimate the probability that a given number of n individuals in a group of size N would be diagnosed with cancer, the following information is required:
1) Average age of the group and associated 10 year cancer rate
2) Size of the group (N)
3) Number (n) diagnosed with cancer

The calculations are estimates based on the BINOMIAL DISTRIBUTION.
P (at least n) = 1- binomdist (n-1, N, rate, 1)

The following spreadsheet contains two probability tables:
1 – For a Given Average Age: Group size vs. number diagnosed with cancer
2 – For a Given Group Size: Average age vs. number diagnosed with cancer

For the following probabilities, the assumed average age of Latin American leaders is 60 (10.13% cancer rate).
Note that Castro was diagnosed in 2006.

-The probability is 0.26% (1 in 389) that at least SEVEN of ALL 20 Latin American leaders would be diagnosed with cancer. Including Castro, the probability is 0.05% (1 in 2203) that 8 would be diagnosed.

-Assuming 10 leftist leaders, the probability that AT LEAST 5 would be diagnosed with cancer is approximately 0.17% (1 in 577). The probability that AT LEAST 6 would be diagnosed is approximately 0.02% (1 in 6330).

-Assuming 14 leftist leaders, the probability that AT LEAST 5 would be diagnosed with cancer is approximately 0.97% (1 in 103). The probability that AT LEAST 6 would be diagnosed is approximately 0.16% (1 in 634).

-Assuming 18 leftist leaders, the probability that AT LEAST 5 would be diagnosed with cancer is approximately 2.96% (1 in 34). The probability that AT LEAST 6 would be diagnosed is approximately 0.68% (1 in 146).

Data Source: National Cancer Institute (SEER)

 
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