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A 26-year-old woman comes to the office with her husband for prenatal counseling. She has a 3-year-old boy with cystic fibrosis from a previous marriage. The patient remarried last year and recently became pregnant. The patient and her current husband are healthy. However, they are worried their unborn child may develop cystic fibrosis. Paternal genetic analysis reveals mutation in only one copy of the *CFTR *gene. What is the probability this couple’s child will have cystic fibrosis?

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Probability is the chance that an event or outcome will occur, and it’s calculated by dividing the number of times an event happened by the number of times the event could have happened.

For example, let’s say you have one six-sided die and you want to know the probability of rolling a certain number, like a three.

Typically, probability is written with a capital P, and P of A represents the probability of “event A” happening.

In this situation, event A is rolling a 6. Since a die has six sides, there are six possible numbers you could roll, so the probability of rolling a three is 1 divided by 6, or 0.167.

Probability can be written as a decimal or as a percent, so the chance of rolling a three is 0.167 times 100 or 16.7%.

Now, there are eight basic rules in probability.

The first rule states that the probability of event A can range anywhere from 0 - or 0% - to 1 - or 100%.

The larger the probability is, the higher the chance that the event will occur.

The second rule states that the sum of the probabilities of all possible outcomes has to equal 1.

For example, the probability of rolling each side of the die is 0.167, and when we add up 0.167 six times, it equals 1.

Sometimes we might want to find the probability that an event won’t occur - like if we wanted to figure out the probability of not rolling a three.

The probability of an event not occurring is called the complement, and it’s written as the probability of the event, except it has a prime symbol - which is just an apostrophe.

The third rule of probability states that the probability that an event doesn’t occur is 1 minus the probability that it does occur.

So, the probability of not rolling a three is 1 minus 0.167, or 0.833.

Turning that around, it also means that the probability of the event occurring equals 1 minus the complement. This is helpful in situations where we want to figure out the probability that an event occurs, but only know the probability that the event won’t occur.

Rule 4 has to do with finding the probability of two or more events happening, which is called a compound event.

For example, let’s say we want to know the probability of rolling a 3 or rolling a 5. In this case, rolling a three is the first event, or event A, and rolling a 5 is the second event, or event B, so the probability of A or B is a compound event.

Now, there are two types of compound events, and the first type is the union of two events, which is the probability of A or B occurring.

Typically it’s written with the union symbol, which looks like a small U.

In a union of two events, the two events can either be disjoint - or mutually exclusive - or not disjoint - or not mutually exclusive.

So, if event A is rolling a 3 and event B is rolling a 5, then A and B are disjoint events, because it’s impossible to roll a 3 and a 5 number at the same time.

Disjoint events are often represented by two circles - one for event A and one for event B - sitting side by side, with no overlapping area.

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