Consider the following newspaper extract: Derby and Nottingham have played 2000200 football matches against each other...

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Consider the following newspaper extract: Derby and Nottingham have played 2000200 football matches against each other in total, each game either at Derby or at Nottingham, and either in sunny or rainy weather. Derby wins more often in rainy weather than sunny weather, in each city. Derby wins 30% of its games played in rainy Derby. Nottingham wins or draws 50% of its games played in sunny Nottingham. A million games took place in rainy Derby and a million games took place in sunny Nottingham." (a) Partition the sample space of 2000200 football match results' into four appropriately chosen sets B1, B2, B3, B4, clearly defining each set. (b) Constructing an annotated 2 by 2 grid, or otherwise, list the four entries of the form (P(B), P(Derby wins B;)) for each value 1< i< 4. Invent any reasonable values for each piece of information missing from the newspaper extract, (if any missing information exists). (c) Calculate P(Derby wins). (d) Calculate P(Derby wins | it rains). (e) Calculate P(Derby wins it is sunny). (f) Calculate P(it rains Derby loses). (g) Does rainy weather favour Team Derby? Explain any apparent contradictions produced by your answers to the previous sections. Consider the following newspaper extract: Derby and Nottingham have played 2000200 football matches against each other in total, each game either at Derby or at Nottingham, and either in sunny or rainy weather. Derby wins more often in rainy weather than sunny weather, in each city. Derby wins 30% of its games played in rainy Derby. Nottingham wins or draws 50% of its games played in sunny Nottingham. A million games took place in rainy Derby and a million games took place in sunny Nottingham." (a) Partition the sample space of 2000200 football match results' into four appropriately chosen sets B1, B2, B3, B4, clearly defining each set. (b) Constructing an annotated 2 by 2 grid, or otherwise, list the four entries of the form (P(B), P(Derby wins B;)) for each value 1< i< 4. Invent any reasonable values for each piece of information missing from the newspaper extract, (if any missing information exists). (c) Calculate P(Derby wins). (d) Calculate P(Derby wins | it rains). (e) Calculate P(Derby wins it is sunny). (f) Calculate P(it rains Derby loses). (g) Does rainy weather favour Team Derby? Explain any apparent contradictions produced by your answers to the previous sections.