Conditional Probability SHIWEI LAN Introduction Definition Examples 1

Conditional Probability SHIWEI LAN

Introduction

Definition

Examples 1. A pair of fair four-sided dice is rolled and the sum is determined. Let A be the event that a sum of 3 is rolled, and let B be the event that a sum of 3 or a sum of 5 is rolled. In a sequence of rolls, What is the probability that a sum of 3 is rolled before a sum of 5 is rolled? (A) 1/8 (B) 1/3 (C) 3/8 (D) 2/3

Properties

Theorems

Examples 2. At a county fair carnival game there are 25 balloons on a board, of which 10 balloons are yellow, 8 are red, and 7 are green. A player throws darts at the balloons to win a prize and randomly hits one of them. Given that the first balloon hit is yellow, what is the probability that the next balloon hit is also yellow? (A) 9/24 (B) 10/25 What is the probability that two balloons hit are both yellow? (A) (10/25)^2 (B) (10/25)*(9/24)

Multiplication Rule

Examples 1 -1. A pair of fair four-sided dice is rolled and the sum is determined. Let A be the event that a sum of 3 is rolled, and let B be the event that a sum of 3 or a sum of 5 is rolled. What is the probability of rolling a sum of 3 first, and continuing the sequence of rolls, rolling a sum of 3 before rolling a sum of 5? (A) 1/8 (B) 1/3 (C) 1/24 (D) 1/16

Reading Assignments Please Read 1. 4 and 1. 5