Upper bound on a dry weekend

The probability of rain is 40%40\% on Saturday and 70%70\% on Sunday. Without assuming independence, what is the tightest possible upper bound on the probability that it does not rain at all this weekend (no rain on either day)?

Show hints (2)+
  1. A dry weekend is the intersection of "dry Saturday" (0.60.6) and "dry Sunday" (0.30.3).
  2. An intersection can't exceed either event's probability - take the minimum.

Answer

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0.3

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Asked at: Citadel, Two Sigma

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