Question

Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A) .

Answer 1

The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).

What is said to be dependent events?

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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