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Mathematics · Grades 7–10

Two draws with replacement

Replacing the first item keeps the second probability unchanged.

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The key idea

Replacing the first item keeps the second probability unchanged.

P(A then A) = P(A)²; independent draws

Worked examples

A bag has 5 red and 6 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

5/11 × 5/11 = 25/121

25/121

A bag has 1 red and 15 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

1/16 × 1/16 = 1/256

1/256

Try it yourself

  1. A bag has 2 red and 2 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

  2. A bag has 1 red and 2 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

Check your understanding

Answers and marking notes
  1. 1/4

    2/4 × 2/4 = 1/4

  2. 1/9

    1/3 × 1/3 = 1/9

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.