Amira cycles to college. On any given day, the probability that it rains is 0.3.
If it rains, the probability that Amira is late is 0.4. If it does not rain, the probability that Amira is late is 0.1.
Find the probability that Amira is late on a randomly chosen day.
Given that Amira is late on a particular day, find the probability that it rained that day. Give your answer to 3 significant figures.
Assuming that whether Amira is late on one day is independent of whether she is late on another day, find the probability that she is late on exactly one of two consecutive days.
State, with a reason, whether the assumption used in part (c) is reasonable.