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Addition theorem: P(A or B), P(A and B) and complements of two events

This type of question, asked 2 times: May 2022 S1, 4 May 2023 S1. All 2 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    133
    If P(A∪B)=0.7P(A \cup B) = 0.7, P(A∩B)=0.2P(A \cap B) = 0.2, then P(A′)+P(B′)P(A') + P(B') is

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  2. Question 2

    4 May 2023 S1

    116
    Let A and B be two events such that the probability that exactly one of them occurs is 25\frac{2}{5} and the probability that A or B occurs is 12\frac{1}{2}, then the probability of both of them occur together is

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