2. An outdoor theatre is holding a summer gala performance. The theatre owner must decide whether to take out insurance against rain for this performance. The theatre owner estimates that

• on a fine day, the total profit will be \(\pounds 15000\)
• on a wet day, the total loss will be \(\pounds 20000\)

Insurance against rain costs \(\pounds 2000\). If the performance must be cancelled due to rain, then the theatre owner will receive \(\pounds 16000\) from the insurer. If the performance is not cancelled due to rain, then the theatre owner will receive nothing from the insurer. The probability of rain on the day of the gala performance is 0.2
Draw a decision tree and hence determine whether the theatre owner should take out the insurance against rain for this performance.