In order to determine whether or not my managers views are accurate, that it is impossible to select at random 10 ART cycles that did not result in a clinical pregnancy, several types of equations can and will be used. The equations that were used can be viewed below under Equations 1. The data and results from the equation tell us that it is possible to randomly select 10 ART cycles that produce no pregnancy. While it is possible for there to be 10 ART cycles chosen at random with none of them resulting in a clinical pregnancy, it is highly unlikely. The calculated probability for 10 randomly selected ART cycles that result in no pregnancy is roughly 0.0102. That probability is essentially 0 however it is possible therefore proving my manager incorrect. The number of pregnancies per 10 randomly selected cycles can be best described using a binomial distribution. A binomial distribution is the probability distribution of a binomial variable. The binomial random variable in this case is pregnancy. The binomial trial in this case is whether or not a pregnancy is created from an ART cycle. Each trial can result in two outcomes, either a pregnancy or a non-pregnancy (when factoring ectopic pregnancy as a non-pregnancy). The probability of failure or success for an ART cycle doesn’t change for each trial based on the data given therefore a binomial equation can be used to find the probability of randomly selecting 10 ART cycles with no pregnancies. In this scenario, the binomial probability distribution is discrete because each result of an individual ART cycle has its own probability of occurring. For instance, in this scenario, the probabilities of ART cycle results is shown below in Figure 1.

Equation 1

Variable | Probability | Pregnancy | 0.624 | Non-Pregnancy | 0.368 | Ectopic Pregnancy | 0.07 |

Figure 1

Given the following data that 10 ART cycles were selected at random from women who are 40 years old and having 8 of them result in a pregnancy, the probability of this result happening can be found by using the binomial distribution method. The probability in this scenario is 0.000056. The equation to obtain this probability can be seen below as Equation 2.
Given the following data that 10 ART cycles were selected at random from women who are 41 years old and having 0 of them result in a pregnancy, the probability of this result happening can be found by using the binomial distribution method. The probability in this scenario is 0.0899 . The equation that produces this probability can be viewed below in Equation 3.
After comparing the probabilities between the two given scenarios, the more likely scenario to occur is the one that has 10 ART cycles from women who are 41 years old and having 0 of them result in a pregnancy. The probability of this happening is a lot greater than the probability of the other scenario.

Equation 3

Equation 2