Edexcel IGCSE Math B 10.H Independent-Event Probability Question Bank
Practise using tree diagrams to multiply independent-event paths and add alternative routes for combined outcomes.
- Syllabus
- First assessment 2018
- Course
- Math B 4MB1
Practise using tree diagrams to multiply independent-event paths and add alternative routes for combined outcomes.

Ahmed and Hani play a game with 20 numbered balls.
The 20 balls are numbered from 1 to 20.
The balls are put in a bag.
Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag.
If the number is a multiple of 5, Ahmed wins.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 3.
If Hani does not win, Ahmed takes a ball, replaces it, and wins if the number is a multiple of 6.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 4.
If Hani does not win, the game stops and the result is a draw.

The incomplete probability tree diagram for the game is shown below.
Complete the probability tree diagram for Ahmed and Hani's game.
Tree entries:
204,2016;206,2014;203,2017;205,2015.
Marks: B1 for each correct pair. Fractions equivalent to these are accepted; the second pair follows through from the multiples of 3 in part (a).
Determine which player, Ahmed or Hani, is more likely to win the game.
Give a reason for your answer.
P(Ahmed wins)=204+2016×2014×203=25071=0.284.P(Hani wins)=2016×206+2016×2014×2017×205=1000359=0.359.
Answer: Hani is more likely to win because P(Hani wins)>P(Ahmed wins).
Marks: M1, A1, M1, A1, A1 dependent.