Probability tree diagrams GCSE lesson: with and without replacement, at least one

Tree diagrams: practice

Sketch a tree or a grid for each question. Give answers as fractions unless the question says otherwise. The stretch is optional.

Diagnostic question: choose and explain

1. A bag has 4 red and 6 blue counters. Two are taken out, one after the other, without replacement. What is the probability that both are red?
   1. 3/25
   2. 4/25
   3. 11/15
   4. 2/15

Practice questions

1. A fair spinner has 8 equal parts, and 3 of them are red. Drag the marker to P(red) on the probability scale.They drag a marker on a number line from 0 to 1.
2. Two fair coins are flipped. What is the probability of two heads? Give it as a fraction.
3. Two fair dice are rolled and their scores added. What is the probability of a total of 7? Give it as a fraction.
4. A bus is late with probability 0.3 each day, independently. What is the probability that it is late on Monday and not late on Tuesday? Give it as a decimal.
5. Are the two events independent (the first doesn't change the chances of the second)? Sort each pair into its group.They sort 6 items into Independent and Not independent.
6. Two independent events: P(A) = 0.6 and P(B) = 0.7. Sam says the probability that at least one of them happens is 0.6 + 0.7 = 1.3. What is it?
   1. 0.42
   2. 1.3
   3. 0.88
   4. 1
7. A spinner lands on red with probability x, blue with probability 2x and green with probability 0.4. Solve the equation for x, one line at a time.They solve x + 2x + 0.4 = 1 line by line, each line checked as they write it.
8. A bag has 5 red and 3 green sweets. Two are eaten, one after the other. What is the probability that they are different colours? Give it as a fraction.
9. Stretch (Higher): a bag has 4 red and 6 blue counters. Two are taken without replacement. The second one is red. What is the probability that the first was red too? Give it as a fraction.

Support: Sketch the tree. On the first branch, write red over all counters. Take one red out: on the second branch, one fewer red and one fewer counter. Then multiply along the path.

Tree diagrams: exit

Place the probability, then one or two sentences.

1. A fair coin is flipped twice. Drag the marker to the probability of at least one head on the probability scale.They drag a marker on a number line from 0 to 1.
2. Explain why 1/6 + 1/6 is not the probability of at least one six when two fair dice are rolled.

Exit check

Place a probability on the scale, then say why adding goes wrong.

Place the probability of at least one head in two flips of a fair coin on the probability scale.

Tree diagrams: multiply along, add across

Draw a tree or a grid for each question, and write the probability on every branch. Give answers as fractions or decimals, as the question has them.