Edexcel S1 2004 January — Question 6

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2004
SessionJanuary
TopicTree Diagrams
TypeIndependent stages tree diagram

6. One of the objectives of a computer game is to collect keys. There are three stages to the game. The probability of collecting a key at the first stage is \(\frac { 2 } { 3 }\), at the second stage is \(\frac { 1 } { 2 }\), and at the third stage is \(\frac { 1 } { 4 }\).
  1. Draw a tree diagram to represent the 3 stages of the game.
  2. Find the probability of collecting all 3 keys.
  3. Find the probability of collecting exactly one key in a game.
  4. Calculate the probability that keys are not collected on at least 2 successive stages in a game.