After years of observations you have found out that
if it rains on a given day, there is a 60% chance
that it will rain on the next day too.
If it is not raining, the chance of rain on the next day in only 25%.

The weather forecast for Friday predicts
the chance of rain is 75%.

What is the probability that
*at least one day* of the weekend
will have *no rain*?

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A = Friday
B = Saturday
C = Sunday

# rain on Friday
P(A)    = 0.75

# no rain on Friday
P(A')   = 1 - P(A)
        = 0.25

P(B|A)  = 0.60  # rain on Saturday given the event of rain on Friday
P(B|A') = 0.25  # rain on Saturday given the event of no rain on Friday

P(C|B)  = 0.60  # rain on Sunday given the event of rain on Saturday
P(C|B') = 0.25  # rain on Sunday given the event of no rain on Saturday

P(B)   = P(B|A) P(A) + P(B|A') P(A')
       = 0.60 * 0.75 + 0.25 * 0.25
       = 0.5125

P(B')  = 1 - P(B)
       = 0.4875

P(C)   = P(C|B) P(B) + P(C|B') P(B')
       = 0.60 * 0.5125 + 0.25 * 0.4875
       = 0.429375

P(C')  = 1 - P(C)
       = 0.570625

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# Bayes' theorem
          P(C|B) P(B)
P(B|C) = -------------
              P(C)

          0.60 * 0.5125     164
P(B|C) = --------------- = -----
             0.429375       229

                                                 164         123     277
1 - P(B and C) = 1 - P(B|C) P(C) = 1 - 0.429375 ----- = 1 - ----- = -----
                                                 229         400     400