1 An amateur weather forecaster describes each day as either sunny, cloudy or wet. He keeps a record each day of his forecast and of the actual weather. His results for one particular year are given in the table,
| \multirow{2}{*}{} | Weather Forecast | \multirow{2}{*}{Total} |
| | Sunny | Cloudy | Wet | |
| \multirow{3}{*}{Actual Weather} | Sunny | 55 | 12 | 7 | 74 |
| Cloudy | 17 | 128 | 29 | 174 |
| Wet | 3 | 33 | 81 | 117 |
| Total | 75 | 173 | 117 | 365 |
A day is selected at random from that year.
- Show that the probability that the forecast is correct is \(\frac { 264 } { 365 }\).
Find the probability that
- the forecast is correct, given that the forecast is sunny,
- the forecast is correct, given that the weather is wet,
- the weather is cloudy, given that the forecast is correct.