1. Samuel Chukwuemeka (Samdom For Peace) Bayes’ Theorem

2. Objectives Students will: Learn the meaning of Conditional Probability Understand Bayes’ Theorem Solve problems using Bayes’ Theorem

3. Conditional Probability Conditional Probability is defined as the probability that an event will occur, given that another event has occurred. It is denoted and read as: P(A | B) means the probability that event A will occur, given that event B has occurred.

4. Bayes’ Theorem Is a mathematical formula that is used for calculating conditional probabilities. It is expressed as: P(A | B) = P(A n B) P(B) Where P(B n A) is the probability of the intersection of events A and B P(B) is the probability of event B

5. Solved Examples Use the Titanic mortality data in the accompanying table. (1.) If someone who was aboard the Titanic was selected, what is the probability of getting a man, given that the selected person died? (2.) What is the probability of getting a boy or girl, given that the randomly selected person is someone who survived?

6. Let’s Define Variables Let Men = M Let Women = W Let Boys = B Let Girls = G Let Survived = S Let Died = D Let Sample Space = Total

7. Let’s Calculate These Variables n(M) = 322 + 1360 = 1682 n(W) = 318 + 104 = 422 n(B) = 29 + 35 = 64 n(G) = 27 + 18 = 45 n(S) = 322 + 318 + 29 + 27 = 696 n(D) = 1360 + 104 + 35 + 18 = 1517 n(Total) = 696 + 1517 = 2213

8. Objectives P(M | D) = P(M n D) P(D) P(D) = 1517P(M n D) = 1360 2213 2213 Therefore, P(M | D) = 1360 / 1517 22132213 P(M | D) = 1360 1517 P(M | D) = 0.897

9. Objectives Students will: Learn the meaning of Conditional Probability Understand Bayes’ Theorem Solve problems using Bayes’ Theorem

10. Objectives Students will: Learn the meaning of Conditional Probability Understand Bayes’ Theorem Solve problems using Bayes’ Theorem