Download conditional probability

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Indeterminism wikipedia, lookup

History of randomness wikipedia, lookup

Randomness wikipedia, lookup

Probabilistic context-free grammar wikipedia, lookup

Dempster–Shafer theory wikipedia, lookup

Infinite monkey theorem wikipedia, lookup

Probability box wikipedia, lookup

Boy or Girl paradox wikipedia, lookup

Ars Conjectandi wikipedia, lookup

Birthday problem wikipedia, lookup

Inductive probability wikipedia, lookup

Probability interpretations wikipedia, lookup

Conditioning (probability) wikipedia, lookup

Conditional Probability and Independence
Learning Targets
I can use the multiplication rule for independent
events to compute probabilities.
2. I can compute conditional probabilities.
Conditional Probability
The probability that one event happens given that
another event is already known to have happened
is called a conditional probability. Suppose we
know that event A has happened. Then the
probability that event B happens given that event
A has happened is denoted by P(B A).
Independent Events
Two events A and B are independent if the
occurrence of one event has no effect on the chance
that the other event will happen. In other words
events a and B are independent if P(A | B) = P(A)
and P(B | A) = P(B).
Dependent Events
Multiplication rule for independent events.
If A and B are independent events, then the
probability that A and B both occur is
General Multiplication Rule
Conditional Probability Formula
To find the conditional probability P(B A), use the formula
First Trimester Screen
The First Trimester Screen is a noninvasive test given during the first
trimester of pregnancy to determine if there are specific chromosomal
abnormalities in the fetus. According to a study published in the New
England Journal of Medicine in November 2005, approximately 5% of
normal pregnancies will receive a positive result. Among 100 women
with normal pregnancies, what is the probability that there will be at
least 1 false positive?