If today is sunny, what is the probability that day after tomorrow will be cloudy? I came across this problem and suspect that the language of the problem is faulty. Does one assume the probability of it being sunny the first day 0.7 ? Are there three days in this problem? What would a tree diagram look for this problem? My working for part a) S-S-C+ S-C-C (0.7*0.7*0.3 + 0.7*0.3*0.6) b) S-S-C + S-C-S (0.7*0.7*0.3 + 0.7*0.3*0.4) Here is the problem: Meteorological data shows that if today is sunny weather, then probability that tomorrow also will be sunny is 0.7, and in case if today is cloudy, then tomorrow will be sunny with a 0.4 probability. a) If today is sunny, find the probability that day after tomorrow will be cloudy b) If today is sunny, find the probability that only one of the next two days will be sunny

Let today, tomorrow and the day after tomorrow correspond with $0,1,2$ respectively.

Then in your work on a) you actually calculate $\Pr(S_0\cap C_2)$ under your own (hence questionable) assumption that $\Pr(S_0)=0.7$.

However, you are asked to calculate $\Pr(C_2\mid S_0)$.

You make the same mistake in b).

Dividing both original answers by $\Pr(S_0)$ will repair.

This comes to the same as striping away the first 0.7 (as TonyK) suggests in his comment.