5 Each day John either cycles to work or goes on the bus.
- If it is raining when John is ready to set off for work, the probability that he cycles to work is 0.4.
- If it is not raining when John is ready to set off for work, the probability that he cycles to work is 0.9 .
- The probability that it is raining when he is ready to set off for work is 0.2 .
You should assume that days on which it rains occur randomly and independently.
- Draw a tree diagram to show the possible outcomes and their associated probabilities.
- Calculate the probability that, on a randomly chosen day, John cycles to work. John works 5 days each week.
- Calculate the probability that he cycles to work every day in a randomly chosen working week.