There is a test that can be performed on a pregnant women to determine if the fetus has the genetic condition known as Trisomy 21, which causes Down Syndrome. The test performs well: for fetuses with Trisomy 21, the test is positive with probability 0.9914, and for fetuses without Trisomy 21, the test is only positive with probability 0.0006. Assume that the probabilityof a fetus carrying Trisomy 21 is 0.001. What are the following quantities?a. P(Positive Test|Fetus has T21)b. P(Positive Test|Fetus does not have T21)c. P(Fetus does not have T21)d. P(Fetus has T21|Positive Test)If a woman receives a positive test result for Trisomy 21, what is the probability that her fetus has Trisomy 21?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
There is a test that can be performed on a pregnant women to determine if the fetus has the genetic condition known as Trisomy 21, which causes Down Syndrome. The test performs well: for fetuses with Trisomy 21, the test is positive with probability 0.9914, and for fetuses without Trisomy 21, the test is only positive with probability 0.0006. Assume that the probability
of a fetus carrying Trisomy 21 is 0.001. What are the following quantities?
a. P(Positive Test|Fetus has T21)
b. P(Positive Test|Fetus does not have T21)
c. P(Fetus does not have T21)
d. P(Fetus has T21|Positive Test)
If a woman receives a positive test result for Trisomy 21, what is the probability that her fetus has Trisomy 21?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
