Probability that weather is fine

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

Find the probability that 2 october is fine and the probability that 3 october is fine.

P(2oct is fine and 3oct is fine)=0.75(0.8)(0.8)=0.48

but answer states 0.56

Also, I need help with: Find the conditional probability that 3 October is rainy, given that 1 October is fine.

Re: Probability that weather is fine

You have F for fine and R for rainy, then

Now

Iterate twice

Re: Probability that weather is fine

Quote:

Originally Posted by

**pickslides** You have F for fine and R for rainy, then

Now

Iterate twice

Sorry, but I don't fully understand your solution.

Am I right to say F (n+1) means the probability that oct 2 is a fine day? What about october 3 then?

Re: Probability that weather is fine

Quote:

Originally Posted by

**Punch** Sorry, but I don't fully understand your solution.

Am I right to say F (n+1) means the probability that oct 2 is a fine day? What about october 3 then?

Yep, thats the way!

Use the results from oct 2 to find for oct 3. same formula.

Re: Probability that weather is fine

Quote:

Originally Posted by

**pickslides** Yep, thats the way!

Use the results from oct 2 to find for oct 3. same formula.

You stated F(n+1) = 0.8F(n)+0.4R(n)

Why is it that R(n) has to be included? Why is it not F(n+1)=0.8F(n)

Re: Probability that weather is fine

Quote:

Originally Posted by

**Punch** You stated F(n+1) = 0.8F(n)+0.4R(n)

Why is it that R(n) has to be included? Why is it not F(n+1)=0.8F(n)

Because a fine day can preceed both a fine day or a rainy day.

Re: Probability that weather is fine

Quote:

Originally Posted by

**pickslides** Because a fine day can preceed both a fine day or a rainy day.

I see... I can't believe I overlooked that!

P(Fine on oct 2 & oct 3)= P(FFF)+P(RFF) =0.75(0.8)(0.8)+0.25(0.4)(0.8)=0.56

But there's still a second part I have a problem with in post 1

Re: Probability that weather is fine

Have you looked at ?

Re: Probability that weather is fine

Its the exact same forumla pickslides gave you. Except instead of oct 1 being a 75/25 split (Fn=.75 and Rn=.25) you know its clear. So Fn=1.0 and Rn =0.0

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Re: Probability that weather is fine