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The probability that it is sunny on any day in January is $0.3$. Find the probability that for two days in January

a) it will be sunny on both days.

b) it will be sunny on one of these days.

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    $\begingroup$ Any thoughts? Note: the problem can not be answered without information regarding dependence. Presumably you are meant to assume independence, though that should be stated (and it isn't clear that it is a realistic assumption). $\endgroup$ – lulu Jun 6 '18 at 13:11
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a) For independent events:
$P(A \cap B) = P(A) * P(B) $ $ \therefore P(\text{2 given days will both be sunny}) = 0.3 * 0.3 = 0.09 $

b) for mutually exclusive events: $P(A \cup B) = P(A) + P(B) $ $ \therefore P(\text{2 given days, at least one is sunny}) = 0.3 + 0.3 = 0.6 $

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