Drawing a probability tree without replacement Revision Card

AI generatedProbabilityKS3 / GCSE

Drawing a probability tree without replacement.

At each split, the outgoing probabilities sum to 1.
Multiply along a route; add mutually exclusive routes that meet the question.
Without replacement, update the counts and total for the second draw.

Example 1

A bag contains 2 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Example 2

A bag contains 3 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Your turn

Question 1

A bag contains 4 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Check answer

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Question 2

A bag contains 5 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Check answer

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Question 3

A bag contains 6 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Check answer

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Question 4

A bag contains 7 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Check answer

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.

Question 5

A bag contains 8 red and 3 blue counters. Two counters are drawn without replacement. Complete the probability tree.

Check answer

Start with the original counts.

After red, remove one red and one from the total.

After blue, red stays the same but the total decreases.

Each pair of branches from the same point sums to 1.