Chance a tree flowers in spring or autumn

Question

In an orchard, a given tree flowers in spring with probability $0.50$ , flowers in autumn with probability $0.30$ , and flowers in both seasons with probability $0.10$ .

What is the probability that the tree flowers at least once during the year (spring or autumn)?

Accepted Answer

"At least once" means it flowers in spring or in autumn or in both. Adding 0.50 and 0.30 counts the both-seasons case twice. Inclusion-exclusion subtracts the overlap once: P(	ext{spring or autumn}) = 0.50 + 0.30 - 0.10 = 0.70. So the tree flowers at least once with probability 0.70. Disjoint check: spring only 0.40, autumn only 0.20, both 0.10, neither 0.30, which sum to 1.00. Takeaway. Even for two events on the same object, add the two chances and subtract the chance of both to get the chance of at least one.

Chance a tree flowers in spring or autumn

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