Probability trees — Notes & Worked ExamplesShow / Hide
Explanation:
On a probability tree diagram, each pair of branches from the same point must add up to 1. Multiply along the branches for AND (P(A and B) = P(A) × P(B)), and add the end probabilities together when more than one path satisfies the question (OR).
Check whether items are picked with replacement (second-pick probabilities stay the same) or without replacement (reduce total denominator by 1 on the second branches, and reduce the numerator by 1 if that colour was already picked).
Example 1: The probability Sam passes his theory test is 0.8 and practical test is 0.6. Find the probability he passes only one test.
Work out A bag contains Red and Blue counters. A counter is picked, replaced, and another is picked. Find the probability of picking exactly 1 Red counter.
Worked Solution & Answer
Probability = successful outcomestotal possible outcomes (all mutually exclusive outcomes add up to 1). 0.42
Answer:0.42
Question 2
[2 marks]
A biased coin is flipped twice. The probability of Heads is 0.3.
(a)Complete the probability tree.[1 mark]
(b)What is the probability of getting two Heads?[1 mark]
Worked Solution & Answer
(a)
Branches: 0.3, 0.7
Answer (a):Branches: 0.3, 0.7
(b)
0.09
Answer (b):0.09
Question 3AQA Jun 2025 2F Q19
[3 marks]
Two spinners each have only red sections and green sections. Spinner 1: P(red) = 38 Spinner 2: P(red) = 15
(a)Complete the tree diagram.[2 marks]
(b)Both spinners are spun. Work out the probability that both spinners land on red.[1 mark]
Answer
Worked Solution & Answer
(a)
Spinner 1 green = 1 – 3/8 = 5/8. Spinner 2 green = 1 – 1/5 = 4/5 M1 A1
Answer (a):Spinner 1 Green = 5/8; Spinner 2 Green = 4/5 (in both positions)
For her lunch, Gina sometimes eats a salad and sometimes drinks a coffee. The probability she eats a salad for lunch on a given day is 0.4. The probability she drinks a coffee on a given day is 0.25. Eating a salad for lunch and drinking a coffee are independent.
(a)Complete the following tree diagram.[2 marks]
(b)Calculate the probability that, on a given day, Gina does not eat a salad for lunch but does drink a coffee.[2 marks]
Worked Solution & Answer
(a)
P(does not eat salad) = 1 - 0.4 = 0.6. M1 Since drinking coffee is independent: P(drinks coffee) = 0.25, P(does not drink coffee) = 1 - 0.25 = 0.75 on both salad and no-salad branches. A1
Answer (a):P(not salad) = 0.6; P(coffee) = 0.25 and P(not coffee) = 0.75 on both branch sets.
Tim has two biased coins, coin **A** and coin **B**. He is going to throw both coins. The probability that coin **A** will land on heads is 0.6 The probability that coin **B** will land on heads is 0.55
(a)Complete the probability tree diagram.[2 marks]
(b)Work out the probability that both coins land on heads.[2 marks]
The probability that Thomas gets to work early on Saturday is 0.7 If Thomas gets to work early on Saturday, the probability that he will get to work early on Sunday is 0.9 If Thomas does not get to work early on Saturday, the probability that he will get to work early on Sunday is 0.6
(a)Use this information to complete the probability tree diagram.[2 marks]
(b)Work out the probability that Thomas gets to work early on both Saturday and Sunday.[2 marks]
Worked Solution & Answer
(a)
Saturday not early = 0.3 M1 Sunday branches = 0.9, 0.1 and 0.6, 0.4 A1
Answer (a):Saturday not early = 0.3; Sunday branches = 0.9, 0.1 and 0.6, 0.4
