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The probability that it rains is 0.5 and that of heavy winds is 0.6 What is the probability that neither happens if the probability of both rain and heavy winds is 0.2

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The probability that it rains is P(R) = 0.5 and the probability of heavy winds is P(W) = 0.6. From this we can derive that the probability of it not raining is P(nR) = 1 - P(R) = 1 - 0.5 = 0.5 and the probability of heavy winds not occurring is P(nW) = 1 - P(W) = 1 - 0.6 = 0.4.

The probability of both events taking place together is P(W & R) = 0.2. This gives the probability of neither of the events taking place together as P(nR & nW) = 1 - 0.2 = 0.8.

The probability of it no rain as well as no heavy winds is P(nW) + P(nR) - P(nR & nW) = 0.5 + 0.4 - 0.8 = 0.1

There is a 10% probability that it neither rains nor are there heavy winds.

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