Chances of Getting Pregnant: Math Estimates the Answers

Panda Conceived after Fertility Monitoring : image by dbking (David)

This giant panda conceived after fertility monitoring: Image by dbking

Once you decided to try to conceive (TTC), you probably asked, “How long to get pregnant?” or “How many monthly cycles should it take to get pregnant?” Some published research states a probability, literally answering the question, “What are the chances of getting pregnant?” Math can help you estimate the answer to these questions, but only with probability rather than certainty. (In other words, there’s no guarantee.)

Limits When Predicting How Long it Will Take to Conceive

Three disclaimers must be clear from the start, in estimating the length of time it will take any family to conceive.

  1. If you or your partner have medical conditions or differ from “the normal” study participant in any way, including age, diet, stress level or any other variable, then the numbers probably won’t fit your situation.
  2. In this article, we approach the research results with one math formula, but there may be more appropriate mathematical models for fertility based on a different set of variables.

Chances of Getting Pregnant: Different Estimates

It’s easy to find an estimate for the chance of getting pregnant. It’s more difficult to know what to believe.

There are multiple articles floating around the Internet reporting on “a study” claiming that 1/4 of couples get pregnant the first month they try, or that the chances are 20% – but none of the articles contain a reference to the study authors, title, or the journal in which it was published.

Another article, How Long it takes to Get Pregnant, claims that “30 percent get pregnant the first cycle” – also with no statistics to back up the claim.


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Rather than try to choose the correct probability, let’s run the math three times, using 20%, 25% and 30% as the chances to conceive in any one monthly cycle.

The Math to Conceive a Child: the Geometric Probability Distribution

Standard Deviation of a Geometric Probability Distribution : image by Mike DeHaan

Standard Deviation of a Geometric Probability Distribution : Image by Mike DeHaan

A “Bournoulli trial” is one attempt to succeed where each try in that series has the same, independent probability of success. The geometric probability distribution is the model for this process of calculating the likelihood of success precisely in the nth trial.

The math is the same whether the success is conceiving a child, drawing an ace from a deck of cards, or winning a jackpot in a lottery. The probability of success may differ, but the process of calculating is the same.

Let’s admit the possibility that this distribution might not describe the chance to conceive for a group of women. If some couples are “more fertile,” they would likely conceive sooner. There may be reasons explaining the delay for those who don’t get pregnant as quickly; they might not have the same basic probability of success.

The simplified definitions and math formulas for the geometric probability distribution are:

  • Let p=P(n) be the “probability of success” at precisely the nth trial. This will be a percentage (eg 20%) or decimal fraction (‘0.20’).
  • The “expected value” is “1/P(n)”. For example, a 20% probability of success is 1-in-5; so the expected value of a 1/5 chance is 5.
  • The “standard deviation”, also called “sigma” (‘σ’) by statisticians, is “( (1-p)/(p2) )1/2“, as seen in the above image.

This spreadsheet shows these three scenarios. Where the probability is 20%, 25% or 30%, then the expected number of monthly cycles to become pregnant should be 4, 3 or 2-3 months for those probabilities.

Click to Read Page Two: Chances of Conceiving In a Cycle – By The Math

© Copyright 2013 Mike DeHaan: Math, All rights Reserved. Written For: Decoded Pregnancy

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