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José travels to school by bus. Each day, the probability that José misses his bus is \(\frac{1}{3}\).

If he misses his bus, the probability that he is late for school is \(\frac{7}{8}\).

If he does not miss his bus, the probability that he is late is \(\frac{3}{8}\).

Let \(E\) be the event "he misses his bus" and \(F\) the event "he is late for school".

The information above is shown in the following tree diagram.

1. Find
   1. \(P(E \cap F)\)
   2. \(P(F)\)
2. Find the probability that
   1. José misses his bus and is not late for school;
   2. José missed his bus, given that he is late for school.

The cost for each day José takes the bus is 3 euros. José goes to school on Monday and Tuesday.

3. Copy and complete this probability distribution table.

   

4. Find the expected cost over the two days for José.