Calculating probabilities is extremely important in genetics. Probabilities predict the likelihood that certain events will occur such as the inheritance of a particular trait in an organism. This can help plant and animal breeders develop more desirable characteristics in their products. It can also help to predict patterns of inheritance of traits and diseases in family lines.

There are a few basic math skills and rules of probability that should be learned before attempting any probability problems.

1) The probability (P) of an event can be thought of as the likelihood that an event will occur. So, probability (P) = the number of times an event is observed (s) divided by the total number of observations (n).

**P(event) = s/n**

For example, in this animation we want to know the likelihood that a dog chosen at random from your study population will have blue eyes. In your population there are a total of 30 dogs. Ten of the dogs have blue eyes and 20 of the dogs have brown eyes. So,

P(dog has blue eyes) = 10/30 = 0.33 or 33%

P(dog has brown eyes) = 20/30 = 0.67 or 67%

Therefore there is a 33% probability that a dog chosen at random from your sample will have blue eyes and a 67% probability that it will have brown eyes.

*Note that a probability is only as accurate as its number of observations. The more observations you have, the more accurate the probability will be. Also, the probabilities that you calculate for your study population may not be at all representative of dog populations worldwide.

2) The sum of probabilities of all possible events associated with an observation is 1 or 100%. Using the example of dog eye color again:

If we knew that the probability of a dog having blue eyes in our population was 33%, and that blue eyes and brown eyes were the only two possible phenotypes, we could calculate the probability that a dog in our study would have brown eyes as P(dog has brown eyes) = 100% - P(dog has blue eyes) = 100% - 33% = 67%.