Two-Way Tables Math Example 3

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Example 3

easy
A two-way table: Left-handed/Male=12, Left-handed/Female=8, Right-handed/Male=88, Right-handed/Female=92. Find the marginal proportion of left-handers and P(Left-handed|Male).

Solution

  1. 1
    Total: 12+8+88+92=20012+8+88+92=200; Left-handed: 12+8=2012+8=20
  2. 2
    Marginal P(Left-handed) =20/200=0.10= 20/200 = 0.10
  3. 3
    Males: 12+88=10012+88=100; P(Left-handed∣Male)=12/100=0.12P(\text{Left-handed}|\text{Male}) = 12/100 = 0.12

Answer

P(Left-handed)=0.10P(\text{Left-handed}) = 0.10; P(Left-handed∣Male)=0.12P(\text{Left-handed}|\text{Male}) = 0.12.
Marginal probability uses the total row or column sum. Conditional probability uses the row (or column) sum as the denominator. The slight difference (12% vs 10%) suggests handedness and gender may be weakly associated.

About Two-Way Tables

A table that displays frequencies for two categorical variables simultaneously, organized with one variable in rows and the other in columns. It shows joint frequencies (individual cells), marginal frequencies (row/column totals), and enables calculation of conditional frequencies.

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More Two-Way Tables Examples

Example 1 medium

A two-way table shows: Smoker/Cancer=30, Smoker/No-Cancer=70, Non-smoker/Cancer=20, Non-smoker/No-Ca

Example 2 hard

From a 2×2 table: Group/Outcome frequencies: A-Success=40, A-Fail=10, B-Success=25, B-Fail=25. Test

Example 4 hard

Construct a two-way table from this information: 200 students surveyed; 120 prefer online learning;

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