AI generatedProbabilityCourse skill

Comparing with-replacement and without-replacement probabilities

Comparing with-replacement and without-replacement probabilities.

  • 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. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.

Example 2

A bag contains 3 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.

Your turn

Question 1

A bag contains 4 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
Check answer
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.
Question 2

A bag contains 5 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
Check answer
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.
Question 3

A bag contains 6 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
Check answer
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.
Question 4

A bag contains 7 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
Check answer
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.
Question 5

A bag contains 8 red and 3 blue counters. Compare with and without replacement.

Two-stage probability treeFirstSecondRRBBRB
Check answer
With replacement, the second bag is unchanged.Without replacement, one red and one counter are removed.
With replacement . Without replacement . The chance is lower without replacement.
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