Drawing a probability tree with replacement Revision Card

AI generatedProbabilityKS3 / GCSE

Drawing a probability tree with 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 with replacement, mixing between draws. Complete the probability tree.

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Check answer

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Check answer

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Check answer

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Check answer

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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 with replacement, mixing between draws. Complete the probability tree.

Check answer

Start with the original counts.

Replacement restores the original bag.

The same probabilities apply after blue.

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