11F Conditional Probability

Conditional probability Conditional probability is where the probability of an event is conditional on (i.e. depends on) another event occurring first. This usually reduces the event space and, therefore, increases the probability.

Conditional probability equation For two events A and B, the conditional probability of event A given that event B occurs is denoted by Pr(A│B) and is given by: Event B is sometimes called the reduced event space. Venn diagrams, tree diagrams, and Karnaugh maps are useful aids in conditional probability.

Example: Exercise 11F, question 1 If Pr(A) = 0.8, Pr(B) = 0.5, and Pr (A ∩ B) = 0.4, find Pr (A │B) and Pr (B │A)

Example, Exercise 11F, question 9 If Pr(A) = 0.7, Pr(B) = 0.5, and Pr (A U B) = 0.9, calculate Pr(A ∩ B) and Pr (B │A)

Example, Exercise 11F, question 17 A group of 60 adventurers includes 30 mountain climbers and 45 scuba divers. Every adventurer does at least one of these activities. How many adventurers are both climbers and divers? Show the information on a Venn diagram. What is the probability that a randomly selected group member is a scuba diver only? What is the probability that a randomly selected adventurer is a scuba diver given that the adventurer is a mountain climber?

Solution

or

Questions for Exercise 11F 2, 5, 9, 12, 16, 19, 21