[Math] Rainy day probability problem

Question

In Vancouver, the probability that a rainy day is followed by another rainy day is $0.5$. The probability that a sunny day is following a by rainy day is $0.7$. Find the probability of:

1. $2$ sunny days, and then $1$ rainy day
2. $2$ rainy days, and then $2$ sunny days
3. Rain 2 days later

What I have so far is

1. $(0.7)(0.7)(0.5)$
2. $(0.5)(0.5)(0.7)(0.7)$

Do I have the right idea on how to find these probabilities? I am assuming independence of events.

Answer 1

HINT

• 1) for the first sunny day p=1, thus p=0.3*0.7
• 2) for the first rainy day p=1, thus...