Straight Thoughts 166 - condom probabilities

Do you remember the saying: “Lotteries are a tax on people who failed math?”

This reflects the fact that people who are not informed about probabilities are the ones who (in average) donate money to the government by gambling.

The same can be said for people who gamble with SDTs and HIV by having promiscuous sex and using condoms as “protection”. The result of this type of gambling, however, can be deadly.

HLI International highlighted this fact visually through a billboard posted in Dar Es Salaam (Tanzania), which raised some eyebrows (see picture on the right). We wrote previously on this subject, pointing out the math. It is commonly accepted that at least one out of twelve condoms fails. That is a failure rate of one 12th, or about eight percent.

However, the probability of infection raises with the number of sexual encounters with an infected person.

This is not a “yearly” rate of infection, but a probability of getting infected with each sexual encounter.

Here we assume that when you have a sexual encounter with an infected person and a condom fails you do get infected. If you just “hope” not to get infected, then what is the condom for?

The probability of survival (which we are interested in) is calculated by multiplication. We can show that after 8 encounters with an infected person (or persons), the probability of being virus-free, when using condoms, is lower than the probability of having caught a virus.

Considering that some promiscuous people would cumulate eight sexual encounters in a matter of days, the poster is dramatically showing the longer term consequences of promiscuous behaviour.

I cannot refrain from mentioning here that in the early 90’s, I participated to a CFRB radio debate facing then councilor Jack Layton (now leader of the federal NDP) to discuss this issue. Since he has no degree in computer science (and I do), he argued, to my astonishment, that probabilities do not multiply, but add up. It took a math teacher calling in to convince the host that Mr. Layton was wrong.

Here is the math:

Probability of infection after one encounter with an infected person: 1/12 = 0.0833. Thus the probability of survival after one encounter with an infected person is 1 - 0.0833 or: 0.9166 (almost 92%).

Probability of survival after two encounters: 0.9166 X 0.9166 = 0.840

After three: 0.840 X 0.9166 = 0.767 (The probability of survival is now only about 76%)

After eight encounters the probability of survival is less than 50%. More exactly: 0.4985

For a shortcut, type 0.916666 on a calculator, then press X(times) =(equal) and do this three times (i.e. 0.916666 to the power of 8) = 0.4985