1 Laura frequently flies to business meetings and often finds that her flights are delayed. A flight may be delayed due to technical problems, weather problems or congestion problems, with probabilities \(0.2,0.15\) and 0.1 respectively. The tree diagram shows this information.
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1. Write down the values of the probabilities \(a , b\) and \(c\) shown in the tree diagram. One of Laura's flights is selected at random.
2. Find the probability that Laura's flight is not delayed and hence write down the probability that it is delayed.
3. Find the probability that Laura's flight is delayed due to just one of the three problems.
4. Given that Laura's flight is delayed, find the probability that the delay is due to just one of the three problems.
5. Given that Laura's flight has no technical problems, find the probability that it is delayed.
6. In a particular year, Laura has 110 flights. Find the expected number of flights that are delayed.