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Conditional probability using expected frequencies

Conditional probability using expected frequencies.

  • Identify the outcomes that are still possible after applying the condition.
  • Use the number or probability meeting both requirements in the numerator.
  • The denominator comes from the restricted sample space, not automatically the original total.

Example 1

= , = and = . Use a model of 1000 outcomes to find .

Expected frequency model
BNot BTotal
A14060200
Not A160640800
Total3007001000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.

Example 2

= , = and = . Use a model of 2000 outcomes to find .

Expected frequency model
BNot BTotal
A294126420
Not A31612641580
Total61013902000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.

Your turn

Question 1

= , = and = . Use a model of 3000 outcomes to find .

Check answer
Expected frequency model
BNot BTotal
A462198660
Not A46818722340
Total93020703000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.
Question 2

= , = and = . Use a model of 4000 outcomes to find .

Check answer
Expected frequency model
BNot BTotal
A644276920
Not A61624643080
Total126027404000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.
Question 3

= , = and = . Use a model of 5000 outcomes to find .

Check answer
Expected frequency model
BNot BTotal
A8403601200
Not A76030403800
Total160034005000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.
Question 4

= , = and = . Use a model of 6000 outcomes to find .

Check answer
Expected frequency model
BNot BTotal
A10504501500
Not A90036004500
Total195040506000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.
Question 5

= , = and = . Use a model of 1000 outcomes to find .

Check answer
Expected frequency model
BNot BTotal
A18278260
Not A148592740
Total3306701000

Black: given data. Blue: working we add.

A and BSplit the expected total along the A then B route.
Not A and BAlso count the other route into B.
Restrict the denominator to the B column.
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