If E and F are independent events such that 0 < P(E) < 1 and 0 < P(F) < 1, then

• A) E and F are mutually exclusive
• B) E and F are independent
• C) E‘ and F’ are independent
• D) P(E|F) + P(E|F’) = 1

To determine the relationship between events E and F, we need to analyze the options based on the definition of independent events. Independent events are those where the occurrence of one does not affect the occurrence of the other.

Analyzing the Options

• A) E and F are mutually exclusive: This is false. If E and F are independent, they can occur together, which contradicts the definition of mutually exclusive events.
• B) E and F are independent: This is true by definition, as stated in the question.
• C) E‘ and F’ are independent: This is also true. The complements of independent events are independent as well.
• D) P(E|F) + P(E|F’) = 1: This is false. This equation does not hold for independent events.

Summary of Findings

The correct statements regarding independent events E and F are options B and C. Therefore, the independence of E and F implies that their complements are also independent.