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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- 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.
- Find the probability that Laura's flight is not delayed and hence write down the probability that it is delayed.
- Find the probability that Laura's flight is delayed due to just one of the three problems.
- Given that Laura's flight is delayed, find the probability that the delay is due to just one of the three problems.
- Given that Laura's flight has no technical problems, find the probability that it is delayed.
- In a particular year, Laura has 110 flights. Find the expected number of flights that are delayed.