Probabilities given that something has happened, from Venn diagrams, two-way tables and tree diagrams.
What you will learn
- Work out a probability given that another event has happened
- Use P(A
- B) = P(A and B) ÷ P(B)
- Solve problems where the second pick depends on the first
Given that
"Given that" shrinks the group you choose from.
From a Venn diagram or table, the denominator is the number in the given group, not the grand total. P(A | B) means the probability of A, given B: the event before the line is the one you want, the one after it is what you already know. So P(B | A) is the probability of B when A has happened. In a two-way table, "given that the person is an adult" means use only the adults row: 5 of 40 adults chose comedy gives 5/40 = 1/8.
- In B: 12 + 18 = 30 people. In both A and B: 12
- P(A | B) = 12/30 = 2/5
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Given that
- From a tree
- Without replacement, given the first pick
- Try it: First question
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Probability
Probabilities of single events, relative frequency, sample spaces, Venn diagrams and two-way tables, tree diagrams, and conditional probability.