You have F for fine and R for rainy, then
Now
Iterate twice
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.
The original question is quoted from "Advanced Level Statistics - J. Crawshaw & J. Chambers, Exercise 3d Tree diagram, Section B, Question 10 (Page 202)."
I had to get through a lot of ambiguous solutions before finally get the answers perfectly matched with those of the textbook.
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 October is fine and the probability that 3 October is fine. answer: 0.7, 0.68
(b) Fine the conditional probability that 3 October is rainy, given that 1 October is fine. answer: 0.28
(c) Find the conditional probability that 1 October is fine, given that 3 October is rainy. answer: 0.65625
(C)
(a)(i)
= =0.7
(ii)
= =0.68
(b)
= =0.28
(c)
= = 0.65625