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Independent events: find an unknown probability or a union using P(A and B) = P(A)P(B)

This type of question, asked 4 times: 10 May 2023 S2, 11 May 2023 S1, 12 May 2024 S1, 19 Apr 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    108
    A and B are independent events with P(A)=310P(A) = \frac{3}{10}, P(B)=25P(B) = \frac{2}{5}, then P(A′∪B)P(A' \cup B) has the value

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  2. Question 2

    11 May 2023 S1

    123
    If A and B are two independent events such that P(A′)=0.75P(A') = 0.75, P(A∪B)=0.65P(A \cup B) = 0.65 and P(B)=pP(B) = p, then value of p is

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  3. Question 3

    12 May 2024 S1

    137
    A and B are independent events with P(A)=14P(A)=\frac{1}{4} and P(A∪B)=2P(B)−P(A)P(A\cup B)=2P(B)-P(A), then P(B)P(B) is

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  4. Question 4

    19 Apr 2025 S2

    144
    Let A and B are independent events with P(B)=25,P(A∪B)=1120P(B) =\frac{2}{5},P(A \cup B) =\frac{11}{20}, then P(A′∣B)P\left( A^{'}\mid B \right) is root of the equation

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