The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).
<h3>What is said to be dependent events?</h3>
When the outcome from one event influences the outcome of the other, two events are referred to as dependent.
- Dependent events in probability are generally real-life events that depend on another event to occur.
- Sam, for example, did well on his math test because he prepared; the gym class used to have a football session even though Adam brought a football from home.
- When you look at these examples, you will realize that one occurrence is dependent on the other.
Derivation of conditional probability from two dependent events P(A and B) is-
The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).
This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.
Step 1: Write the multiplication rule down:
P(A and B) = P(A)*P(B|A)
Step 2: P(A) divides both sides of the equation:
P(A and B) / P(A) = P(A)*P(B|A) / / P(A)
Step 3: On the right side of the equation, cancel P(A):
P(A and B) / P(A) = P(B|A)
Step 4: Rewrite the equation as follows:
P(B|A) = P(A and B) / P(A)
Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).
To know more about the conditional probability, here
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