# True or false

The exercise was created 2023-03-18 by norastillman. Question count: 23.

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• P(B|A) ≤ P(B) false
• P(B|A) + P(B|Ac) = 1 false
• P(B) = P(B ∩A) + P(B ∩Ac) true
• P(A ∪B) + P(A ∩B) = P(A) + P(B) true
• P(A ∩Bc) + P(Ac ∩B) = P(A ∪B) −P(A ∩B) true
• P(A|B) ≥P(A ∩B) true
• If P(A|B) = P(A), then P(B|A) = P(B) true
• P(B|Ac) = 1 −P(B|A) false
• P(A) ≤P(A ∪B) true
• P(A ∪B) + P(A ∩B) = P(A) + P(B) true
• P(A ∩Bc) + P(Ac ∩B) = P(A ∪B) −P(A ∩B) true
• If A and B are disjoint, then they are independent false
• P(A ∩B) ≤P(B) true
• P(A ∪B) ≤P(A) + P(B) true
• If A and B are independent, then P(A ∪B) = 1 −P(Ac)P(Bc) true
• If A and B are independent, then P(A ∪B) = P(A) + P(B) false
• For any events A and B: P(B|Ac) = 1 −P(B|A) false
• For any events A and B: P(B|A) ≤P(B) false
• If X ∼ unif [0, 2], then X2 ∼ unif [0, 4]. false
• If N ∼ geom(p) and X ∼ bin (n, p), then P(N > n) = P(X = 0). true
• If X and Y are independent with the same mean μ and the same variance σ2, then 2X −Y has variance 3 σ2 false
• If X ∼N(μ, σ2), then P(X = x) = φ (x −μ σ false
• If X ∼ bin(n, p), then 2X ∼ bin(2n, p) false

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