A sports event lasts for $4$ days and begins on Sunday. The chance that rain falls on Sunday is $0.4$. For each later day, the chance of rain is $0.7$ if the previous day was rainy and $0.2$ if the previous day was dry.
(a)[1]
Find the probability that there is no rain on any of the $4$ event days.
(b)[2]
Find the probability that Tuesday is the first day of rain during the event.
(c)[3]
Find the probability that rain occurs on exactly one of the 4 days of the event.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Thus $P(\text{no rain})=0.6(0.8)^3=\frac{192}{625}$.” …