# In a simple model of the weather in October, each day is classified as either fine or rainy?

In a simple model of the weather in October, each day is classified as either fine or rainy. The probability that a fine day is followed by a fine day is 0.8. The probability that a rainy day is followed by a fine day is 0.4. The probability that 1 October is fine is 0.75.

a)Find the probability that 2 Oct is fine and the probability that 3 Oct is fine(0.7,0.68)

b)Find the conditional probability that 3 Oct is rainy, given that 1 Oct is fine(0.28)

c)Find the conditional probability that 1 Oct is fine, given that 3 Oct is rainy(0.65625)

Answers are in the brackets

Thanks

### 1 Answer

- PuzzlingLv 72 months ago
I would really like to see you at least trying to solve these yourself rather than posting all your questions and asking for others to show you the work. You even have the answers to see if you are correct.

Let me help you get started.

PART A1:

How can you end up with October 2 being a fine day?

Case 1 - It was fine on Oct 1 (0.75) and then also fine the next day (0.8)

Case 2 - It was NOT fine on Oct 1 (0.25) and then it was fine the next day (0.4)

(0.75 * 0.8) + (0.25 * 0.4) = ??

PART A2:

How can you end up with October 3 being a fine day?

Case 1 - It was fine on Oct 2 (part A1) and then also fine the next day (0.8)

Case 2 - It was NOT fine on Oct 2 (1 - part A1) and then it was fine the next day (0.4)

Work on that and then see if you can continue with the other parts using what you've learned from the answers to your other questions.