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Question Directory
Rain on Weekend
The probability that it will rain on Saturday is 60%, and the probability that it will rain on Sunday is 70%. What is the probability that it will rain on the weekend, if we assume the probabilities are independent?
To solve this problem it is simpler to consider the negation of the probabilities - that is, the probability that it will not rain on either Saturday or Sunday. The probabilities of no rain on Saturday and Sunday are
$$
P(\text{no rain on Sat}) = 1 - 0.6 = 0.4,
$$
$$
P(\text{no rain on Sun}) = 1 - 0.7 = 0.3.
$$
The probability that it will not rain on the weekend is given by
$$
P(\text{no rain on weekend}) = P(\text{no rain on Sat})P(\text{no rain on Sun})
$$
which is
$$
P(\text{no rain on weekend}) = 0.12
$$
So, the probability of it raining on the weekend is
$$
P(\text{rain on weekend}) = 1 - P(\text{no rain on weekend}) = 0.88
$$
or $88\%$.