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P (A/B) Formula. P (A/B) is known as conditional probability and it means the probability of event A that depends on another event B and is read as "probability of A given B". It says P (A/B) = P (A∩B) / P (B).
If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B ", or "the probability of A under the condition B ", is usually written as P (A|B)[2] or occasionally PB(A).
- Dependent Events
- Tree Diagram
- Notation
- Finding Hidden Data
- Big Example: Soccer Game
- Friends and Random Numbers
But events can also be "dependent" ... which means they can be affected by previous events... This is because we are removingmarbles from the bag. So the next event depends on what happened in the previous event, and is called dependent. Dependentevents are what we look at here.
A Tree Diagramis a wonderful way to picture what is going on, so let's build one for our marbles example. There is a 2/5 chance of pulling out a Blue marble, and a 3/5 chance for Red: We can go one step further and see what happens when we pick a second marble: If a blue marble was selected first there is now a 1/4 chance of getting a blue marble a...
We love notation in mathematics!It means we can then use the power of algebra to play around with the ideas. So here is the notation for probability: P(A) means "Probability Of Event A" In our marbles example Event A is "get a Blue Marble first" with a probability of 2/5: P(A) = 2/5 And Event B is "get a Blue Marble second" ... but for that we have...
Using Algebra we can also "change the subject" of the formula, like this: And we have another useful formula: "The probability of event B given event A equals the probability of event A and event B divided by the probability of event A"
You are off to soccer, and want to be the Goalkeeper, but that depends who is the Coach today: 1. with Coach Sam the probability of being Goalkeeper is 0.5 2. with Coach Alex the probability of being Goalkeeper is 0.3 Sam is Coach more often ... about 6 out of every 10 games (a probability of 0.6). So, what is the probability you will be a Goalkeep...
Here is another quite different example of Conditional Probability. 4 friends(Alex, Blake, Chris and Dusty) each choose a random number between 1 and 5. What is the chance that any of them chose the same number? Let's add our friends one at a time ...
Sep 28, 2022 · Given two events, A and B, to “find the probability of A given B” means to find the probability that event A occurs, given that event B has already occurred. We use the following formula to calculate this probability: P (A|B) = P (A)*P (B|A) / P (B) where: P (A|B): The probability of event A, given event B has occurred.
Definition of Conditional Probability. If A and B are two events associated with the same sample space of a random experiment, the conditional probability of event A given that B has occurred is given by P (A/B) = P ( A ∩ B)/ P (B), provided P (B) ≠ 0. Let us understand conditional probability with an example.
If $A$ and $B$ are two events in a sample space $S$, then the conditional probability of $A$ given $B$ is defined as $$P(A|B)=\frac{P(A \cap B)}{P(B)}, \textrm{ when } P(B)>0.$$
Jul 14, 2023 · The probability of event B happening, given that event A already happened, is called the conditional probability. The conditional probability of B, given A is written as P(B|A) P (B | A), and is read as “the probability of B given A happened first.”. We can use the General Multiplication Rule when two events are dependent.
