Suppose that A, B, and D are events such that A and B are independent, Pr(A ∩ B ∩ D) = 0.04, Pr(D|A ∩ B) = 0.25, and Pr(B) = 4 Pr(A). Evaluate Pr(A ∪ B).

Suppose that a random variableX has the binomial distribution with parameters n = 8 and p = 0.7. Find Pr(X ≥ 5)

Suppose that a random variable X has the binomial distribution with parameters n = 15 and p = 0.5. Find Pr(X < 6).