True or false

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

Click