Conditional Probability
Conditional probability measures the likelihood of an event occurring given that another event has already occurred, and is essential for understanding dependent events.
What You Need to Know
Key Concept Diagram
P(A|B) = P(A ∩ B) / P(B) represents the probability of A occurring given B has occurred
Two events are independent if P(A|B) = P(A) — knowing B occurred does not change the probability of A
Two events are dependent if knowing one occurred changes the probability of the other
Two-way tables and tree diagrams are effective tools for organising and solving conditional probability problems
Key Vocabulary
Conditional probability
The probability of an event occurring given that another event has already happened, written P(A|B)
Independent events
Two events where the occurrence of one does not affect the probability of the other
Dependent events
Two events where the occurrence of one changes the probability of the other occurring
Sample space
The set of all possible outcomes of a probability experiment
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
In a group of 100 students, 60 study Maths, 40 study Science, and 20 study both. What is P(Maths | Science)?
Question 2
A bag has 5 red and 3 blue marbles. One marble is drawn and NOT replaced. What is the probability the second marble is red given the first was red?
Question 3
If P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.15, are A and B independent?
Key Concepts Summary
- ●P(A|B) = P(A ∩ B) / P(B) represents the probability of A occurring given B has occurred
- ●Two events are independent if P(A|B) = P(A) — knowing B occurred does not change the probability of A
- ●Two events are dependent if knowing one occurred changes the probability of the other
- ●Two-way tables and tree diagrams are effective tools for organising and solving conditional probability problems