1. Xavier, Yuri and Zara all travel to work in the morning via different methods. The probabilities of them arriving late are, independently, 0.2, 0.1 and 0.35 respectively.

1. Calculate the probability that for a particular day:

1. All three arrive late.

(2 marks)

1. None of the three arrive late.

(2 marks)

1. Only Zara arrives late.

(2 marks)

Another worker, Wei, catches the same bus as Zara but stops off at a shop to buy lunch each morning. The probability that Wei arrives late is 0.85 when Zara arrives late, and is 0.1 when Zara does not arrive late.

1. Calculate the probability that for a particular practice session:

1. Both Zara and Wei arrive late

(2 marks)

1. Either Zara or Wei, but not both, arrives late.