In one country, each day’s weather is put into one of two categories: fine or rainy. The chance that a fine day is followed by another fine day is $0.75$, while the chance that a rainy day is followed by a fine day is $0.4$. The probability that $1$ April is fine is $0.8$. The tree diagram shown below gives the possible weather outcomes for $1$ April and $2$ April.
(a)[1]
Complete the tree diagram by showing the probabilities.
(b)[2]
Find the probability that $2$ April is fine.
(c)[3]
Let $X$ represent the event that $1$ April is fine and let $Y$ represent the event that $3$ April is rainy. Find the value of $P(X \cap Y)$.
(d)[3]
Find the probability that $1$ April is fine given that $3$ April is rainy.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Tree diagram drawn correctly, with all branch probabilities shown” …