Tree diagrams
The Maths Habit Handout to print
A spinner has P(red) = 0.26 and P(blue) = 0.38.
0.64
Find P(red or blue).A spinner has P(green) = 25. It is spun twice.
425
Find P(green both times).P(Kofi’s alarm fails) = 0.1 and P(his bus is cancelled) = 0.3. The two are independent. Find P(both happen).
0.03
A player scores 9 shots out of 10.
What is the chance of 10 in a row?
About 35%
- Tree diagram
- A diagram that shows every outcome of two or more events.
- Independent
- One event does not change the probability of the other.
Tree diagrams
- Draw the branchesTwo branches, then two from the end of each.
- Label every branchThe probabilities on each pair add to 1.
- Multiply along the branchesMultiply the probabilities along each path.
- Add the outcomes you wantTick the ends you want and add them.
The probability a train is late is 0.2. Look at two journeys. Find the probability it is late both times.
A spinner lands on green with probability 310. It is spun twice. Find the probability of exactly one green.
A bag has 2 red and 5 blue counters. One is taken and replaced, then another is taken. Find the probability of (a) two reds (b) different colours. (a) 449 (b) 2049
A seed grows with probability 0.8. Two seeds are planted. Find the probability that (a) both grow (b) exactly one grows. (a) 0.64 (b) 0.32
A bag has 2 red and 5 blue counters. One is taken and replaced, then another is taken. Find the probability of (a) two reds (b) different colours. (a) 449 (b) 2049
A spinner lands on blue with probability 13. It is spun twice. Find the probability of (a) two blues (b) exactly one blue. (a) 19 (b) 49
A bag has 2 red and 5 blue counters. One is taken and replaced, then another is taken. Find the probability of (a) two reds (b) different colours. (a) 449 (b) 2049
Ella hits a target with probability 0.9. She throws twice. Find the probability that she (a) hits both times (b) misses both times. (a) 0.81 (b) 0.01
A bag has 2 red and 5 blue counters. One is taken and replaced, then another is taken. Find the probability of (a) two reds (b) different colours. (a) 449 (b) 2049
A box has 3 lemon and 4 lime sweets. One is taken and replaced, then another is taken. Find the probability of (a) two limes (b) the same flavour.
(a) 1649 (b) 2549
A bag has 2 red and 5 blue counters. One is taken and replaced, then another is taken. Find the probability of (a) two reds (b) different colours. (a) 449 (b) 2049
An ordinary dice is rolled twice. Find the probability of (a) two sixes (b) exactly one six. (a) 136 (b) 518
Answer sheet
A basketball player scores each shot with probability 0.9. She takes 3 shots. Find the probability that she scores all three.
0.729A bag has red and blue counters. One is taken and replaced, then another is taken. The probability of two reds is 19. What is the probability of two blues?
49
A spinner lands on blue or red. P(blue) = 0.4. It is spun twice. Fill in the tree diagram.
0.6; 0.4, 0.6; 0.4, 0.6Find the probability of blue both times.
0.16Find the probability of exactly one blue.
0.48