(a) The weather forecast on December 24 predicts that it will snow in the UK on December 25. 80% of the time when it snows in the UK, the snow has been correctly forecast. When it does not snow in December, January or February, the forecast was incorrectly predicting snow in 10% of the cases. On average it snows in the UK on 23 days of the year in the months of December, January and February. Given this, what is the probability that it will snow on December 25? (b) Consider the same problem as in (a) but suppose that you do not know how many days it snows per year. What would you change in your calculation? Repeat the calculation with this change and give the result. (c) How does the calculation change if you live in England, with only 5 days of snow, while the performance of the weather forecast remains the same.
(a) The weather forecast on December 24 predicts that it will snow in the
UK on December 25. 80% of the time when it snows in the UK, the
snow has been correctly forecast. When it does not snow in December,
January or February, the forecast was incorrectly predicting snow in
10% of the cases. On average it snows in the UK on 23 days of the
year in the months of December, January and February. Given this,
what is the
(b) Consider the same problem as in (a) but suppose that you do not know
how many days it snows per year. What would you change in your
calculation? Repeat the calculation with this change and give the result.
(c) How does the calculation change if you live in England, with only 5
days of snow, while the performance of the weather forecast remains
the same.
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