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Conditional probability from a Venn diagram

Conditional probability from a Venn diagram.

  • The rectangle is the universal set. The overlap belongs to both sets.
  • Fill the overlap first; subtract it from each set total to find the “only” regions.
  • Union means either or both; intersection means both; complement means outside the named set.

Example 1

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB4253
Use only A as the denominator; the overlap meets both conditions.

Example 2

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB5354
Use only A as the denominator; the overlap meets both conditions.

Your turn

Question 1

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB6455
Check answer
Use only A as the denominator; the overlap meets both conditions.
Question 2

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB7556
Check answer
Use only A as the denominator; the overlap meets both conditions.
Question 3

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB8657
Check answer
Use only A as the denominator; the overlap meets both conditions.
Question 4

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB9758
Check answer
Use only A as the denominator; the overlap meets both conditions.
Question 5

A person is chosen at random. Given that they are in A, find .

Two-set Venn diagramξAB10269
Check answer
Use only A as the denominator; the overlap meets both conditions.
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