James surveyed people at school and asked whether $ \quad $ The events "male" and "buys lunch" are not they bring their lunch to school or buy their lunch at independent because school more often. The results are shown below.
Bring lunch: 46 males, 254 females
$ P( $ buys lunch $ \mid $ male $ )=P( $ male $ )=0.4 $.
Buy lunch: 176 males, 264 females
$ P( $ male $ \mid $ buys lunch $ )=P( $ male $ )=0.3 $.
$ P( $ buys lunch $ \mid $ male $ )=0.3 $ and $ P( $ male $ )=0.4 $.
$ P( $ male $ \mid $ buys lunch $ )=0.4 $ and $ P( $ male $ )=0.3 $.

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