Question

Which of these statements is always true if E1 and E2 are events from a finite sample space S?

Option 1: P(E1 ∪ E2) = P(E1) + P(E2)
Option 2: P(E1 ∩ E2) = P(E1) - P(E2)
Option 3: P(E1 ∩ E2) ≤ P(E1) + P(E2)
Option 4: P(E1 ∪ E2) = P(E1) * P(E2)

Answer 1

The statement that is always true if E1 and E2 are events from a finite sample space S is Option 3: P(E1 ∩ E2) ≤ P(E1) + P(E2).

Step-by-step explanation:

The statement that is always true if E1 and E2 are events from a finite sample space S is Option 3: P(E1 ∩ E2) ≤ P(E1) + P(E2).

This statement is known as the addition rule. It states that the probability of the intersection of two events, E1 and E2, is always less than or equal to the sum of their individual probabilities.

In other words, the probability of both events happening together cannot be greater than the sum of their individual probabilities.