Independent stages tree diagram

Questions where the probabilities at each stage are fixed and do not depend on previous outcomes (e.g., die rolls, independent daily events, or sampling with replacement).

1 questions

Edexcel S1 2004 January Q6
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.