4 In a certain country, the weather each day is classified as fine or rainy. The probability that a fine day is followed by a fine day is 0.75 and the probability that a rainy day is followed by a fine day is 0.4 . The probability that it is fine on 1 April is 0.8 . The tree diagram below shows the possibilities for the weather on 1 April and 2 April.
- Complete the tree diagram to show the probabilities.
1 April
\includegraphics[max width=\textwidth, alt={}, center]{33c0bd01-f27b-424c-a78a-6f36178bc08c-08_601_405_706_408}
2 April
Fine
Rainy
Fine
Rainy - Find the probability that 2 April is fine.
Let \(X\) be the event that 1 April is fine and \(Y\) be the event that 3 April is rainy. - Find the value of \(\mathrm { P } ( X \cap Y )\).
- Find the probability that 1 April is fine given that 3 April is rainy.