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marigirl

  • one year ago

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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  1. jim_thompson5910
    • one year ago
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    If the weather is fine on Monday, what is the probability it is fine on Tuesday?

  2. marigirl
    • one year ago
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    4/5

  3. jim_thompson5910
    • one year ago
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    so we have this probability tree so far |dw:1438843602331:dw|

  4. jim_thompson5910
    • one year ago
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    if we extend things out to wednesday, we get |dw:1438843710283:dw|

  5. jim_thompson5910
    • one year ago
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    hopefully you agree and got these same values?

  6. marigirl
    • one year ago
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    Yes. So is it fine monday to Thursday and wet Friday

  7. jim_thompson5910
    • one year ago
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    oh wait I messed up the table, one sec

  8. jim_thompson5910
    • one year ago
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    ok fixed |dw:1438844172501:dw|

  9. jim_thompson5910
    • one year ago
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    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

  10. marigirl
    • one year ago
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    Thanks heaps I started to draw a tree diagram too. I really appreciate your time

  11. jim_thompson5910
    • one year ago
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    I was halfway through drawing it and scrapped it lol. It went off the page. You're welcome.

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