An amateur meteorologist has studied weather patterns for several years, and has determined that id it is fine one day, the probability that is fine the next day is 4/5; whereas if it is wet, the probability that the next day is wet is 1/4. If it is fine one Monday, what is the probability that it is wet on Friday?
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If the weather is fine on Monday, what is the probability it is fine on Tuesday?
so we have this probability tree so far
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if we extend things out to wednesday, we get
hopefully you agree and got these same values?
Yes. So is it fine monday to Thursday and wet Friday
oh wait I messed up the table, one sec
hmm now that I look through this more, a table is going to get very messy as we get to fri
here's a better approach
P(fine on monday) = 1
P(fine on tuesday) = 4/5
P(fine on wednesday) = P(fine on tuesday)*(4/5) + P(wet on tuesday)*(3/4)
P(fine on wednesday) = (4/5)*(4/5) + (1/5)*(3/4)
P(fine on wednesday) = 0.79
P(fine on thursday) = P(fine on wednesday)*(4/5) + P(wet on wednesday)*(3/4)
P(fine on thursday) = (0.79)*(4/5) + (0.21)*(3/4)
P(fine on thursday) = 0.7895
P(fine on friday) = P(fine on thursday)*(4/5) + P(wet on thursday)*(3/4)
P(fine on friday) = (0.7895)*(4/5) + (0.2105)*(3/4)
P(fine on friday) = 0.789475
P(wet on friday) = 1 - 0.789475
P(wet on friday) = 0.210525
Thanks heaps I started to draw a tree diagram too. I really appreciate your time
I was halfway through drawing it and scrapped it lol. It went off the page. You're welcome.