$$\DeclareMathOperator{cosec}{cosec}$$

# Statistics and Probability

## Furthermore

Formula Booklet: 4.13
 Bayesâ€™ theorem $$P(B|A) = \frac{P(B)P(A|B)}{P(B)P(A|B)+P(B')P(A|B')}$$ $$P(B_i|A) = \frac{P(B_i)P(A|B_i)}{P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+P(B_3)P(A|B_3)}$$

Bayes' theorem provides a way to determine the probability of an event occurring based on prior knowledge of conditions that might be related to the event. When considering three events, Bayes' theorem can be applied iteratively to update our beliefs about the probabilities of each event as new evidence is presented.

The general formula for Bayes' theorem is:

$$P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}$$

Where:

$$P(A|B)$$ is the probability of event A given that event B has occurred.

$$P(B|A)$$ is the likelihood of event B occurring given that event A has occurred.

$$P(A)$$ is the probability of event A.

$$P(B)$$ is the probability of event B.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.

For Students:

For All: