Calculating Conditional Probability | A Step-by-Step Guide for Probability Theory.

P(A given B)

In probability theory, the notation P(A | B) represents the conditional probability of event A occurring given that event B has occurred

In probability theory, the notation P(A | B) represents the conditional probability of event A occurring given that event B has occurred. It is read as “the probability of A given B.”

To calculate P(A | B), you need to know the probability of both events A and B occurring, as well as the probability of event B occurring. The formula for conditional probability is as follows:

P(A | B) = P(A and B) / P(B)

Here’s a step-by-step explanation of how to calculate P(A | B):

1. Find the probability of event B occurring, denoted as P(B).

2. Determine the probability of both event A and event B occurring, denoted as P(A and B).

3. Apply the formula mentioned earlier:
P(A | B) = P(A and B) / P(B)

For example, let’s say you want to find the probability of getting a head on a fair coin (event A), given that the coin was flipped and landed on heads (event B).

Step 1: P(B) = 1/2 (since the probability of getting a head on a fair coin is 1/2).

Step 2: P(A and B) = 1/2 (since both events A and B occur simultaneously).

Step 3: Applying the formula:
P(A | B) = (1/2) / (1/2) = 1

Therefore, the probability of getting a head (A) given that the coin landed on heads (B) is 1 or 100%.

This means that if you know event B has occurred (coin landed on heads), then the probability of event A (getting a head) happening is certain.

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