Conditional Probability MDM 4U Lesson 4.4

Given A, how likely is B? In many cases, we want to find the probability of an event given that another event has already happened. This is referred to as conditional probability

General Formula P(B|A) asks “what is the probability of B given A has occurred?" Think of it as "out of all A's, how many are also B's"

Example 1 Suppose that in Vancouver there is a 25% probability that any given day is both cloudy and rainy. It is cloudy 50% of the time. If it is a cloudy day, what is the probability of rain?

Independent vs. dependent When the probability of B is the same regardless of whether A has occurred or not we say that B is independent of A. When B is independent from A Probability of B given A is the same as the overall probability of B

Ex #2: Dice Roll 2 dice. What is the probability of rolling a sum of 7 given that one or more die turn up as a 5? A = turn up a 5 B = roll sum of 7

Ex. #3: In a school of 500 boys and 400 girls, 100 boys and 80 girls participate in the 30 hour famine. Suppose a student has been chosen at random. A= event that a girl is chosen. B= event that a famine participant is chosen. a) Find P(A) b) Find P(B|A)

Ex. #4: What is the probability of drawing two fives in a row from a well shuffled deck of 52 playing cards? The first card drawn is not replaced.

Practice Questions Worksheet Online Page 235 #1 – 6, 8, 9, 11