Independent Events

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: 1 – (1 – P₁)(1 – P₂) 

If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.

If A and B are two independent events then P(A and B) = P(A).P(B).

A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?

One-shot is fired from each of the three guns. Let A, B, and C denote the events that the target is hit by the first, second and third guns respectively. assuming that A, B, and C are independent events and that P(A) = 0.5, P(B) = 0.6, and P(C) = 0.8, then find the probability that at least one hit is registered.

In Question 64 above, P(B|A′) is equal to ______.

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 and P(A' ∩ B') is ______.

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: (1 – P₁) P₂