Tree diagrams

• What is the outcome if the spinner lands on W?

  The player wins
• What is the outcome if the spinner lands on L?

  The player loses
• How many times is Sam going to play the game?

  Twice
• What are all the possible outcomes for Sam's games?

  • Win-Win
  • Win-Lose
  • Lose-Win
  • Lose-Lose
• What is the best outcome for Sam?

  Winning both games
• What is the worst outcome for Sam?

  Losing both games
• What is a probability tree diagram used for?

  Representing outcomes of events
• What are the two outcomes for the first game in the tree diagram?

  Win or Lose
• How many branches are drawn for the first game in the tree diagram?

  Two branches
• What are the two outcomes for the second game in the tree diagram?

  Win or Lose
• How do you label the probabilities on the tree diagram?

  By identifying win and lose outcomes
• What is the probability of winning on the spinner?

  $\frac{2}{5}$
• What is the probability of losing on the spinner?

  $\frac{3}{5}$
• What is the probability of rolling a six on a fair six-sided die?

  $\frac{1}{6}$
• What is the probability of not rolling a six on a fair six-sided die?

  $\frac{5}{6}$
• What are the outcomes when throwing a fair coin?

  Heads or Tails
• What is the probability of getting heads on a fair coin?

  $\frac{1}{2}$
• What is the probability of getting tails on a fair coin?

  $\frac{1}{2}$
• How do you calculate the probability of winning a prize in Ria's game?

  By rolling a six and then tails
• What is the probability notation for rolling a six and then tails?

  P(6T)
• How do you find the probability of a specific route in a tree diagram?

  Multiply the probabilities along the route
• What is the probability of rolling a six followed by tails?

  $\frac{1}{12}$
• What is the total number of counters in the bag?

  Eight counters
• What is the probability of picking a green counter?

  $\frac{3}{8}$
• What is the probability of picking a red counter?

  $\frac{5}{8}$
• What happens to the probabilities when a counter is replaced?

  They remain the same for the second pick
• What is the probability of selecting two red counters?

  $\frac{25}{64}$
• How do you calculate the probability of one red counter?

  Add probabilities of two routes
• What is the probability of one red counter from two picks?

  $\frac{30}{64}$
• What is the probability of both counters being the same color?

  $\frac{34}{64}$
• What is the simplified probability of both counters being the same color?

  $\frac{17}{32}$
• What is the probability of passing the math test?

  $0.8$
• What is the probability of passing the English test?

  $0.7$
• What are the steps to complete a probability tree diagram?

  1. Identify outcomes for the first event
  2. Draw branches for each outcome
  3. Identify outcomes for the second event
  4. Draw branches for each outcome
  5. Label probabilities on the branches
• What is the probability of picking red twice in a row?

  $\frac{25}{64}$
• How do you simplify the probability $\frac{34}{64}$?


  Divide both by 2 to get $\frac{17}{32}$
• What does a tree diagram represent in probability?

  It shows all possible outcomes and their probabilities
• What is the probability that Luke passes the math test?

  0.8
• What is the probability that Luke passes the English test?

  0.7
• How do you calculate the probability of passing both tests?

  Multiply the probabilities: $0.8 \times 0.7$