## Independence in Two Way or Contingency Tables

The two way table below contains some completely fictitious data on the the types of computers favoured by men and women.

| Laptop | Desktop | Tablet | Total |

Men | 31 | 17 | 40 | 88 |

Women | 12 | 42 | 17 | 71 |

Total | 43 | 59 | 57 | 159 |

Events A and B are independent if(1)

For the table above take A as 'a person picked at random favours a desktop', and event B as 'a person picked at random is a woman'.

The probability that a person picked at random favours desktops isand the probability that a person picked at random is a woman is

The number of women who favour desktops is 42 out of a total of 159, so the probability that a person picked at random is a woman favouring a desktop is

These probabilities do not satisfy condition (1) for indepence since