Question

Given any two events, E and E', what does the probability P(E U E') represent?

A) Neither event occurs.
B) Both of the events occur.
C) One of the events occurs, or both occur.
D) One of the events occurs but not both.

Answer 1

The probability P(E U E') represents the likelihood that either event E, event E', or both events happen. For mutually exclusive events, this probability is the sum of their individual probabilities, whereas for non-mutually exclusive events, the probability of both occurring together is subtracted from the sum of their individual probabilities.

Step-by-step explanation:

The probability P(E U E') represents the chance that one of the events occurs, or both occur. To elaborate, if we're considering two events E and E', the union of these events (E U E'), also expressed as P(E OR E'), encapsulates all the outcomes where either event E happens, event E' happens, or both events occur simultaneously. In terms of probability calculation, for mutually exclusive events, this probability would be the sum of their individual probabilities since they cannot both occur at the ame time. However, if the events are not mutually exclusive, we must then subtract the probability of both E and E' occurring together (P(E AND E')), as it is counted twice when we add P(E) and P(E').

For non-mutually exclusive events, the probability that at least one of them occurs is represented by the formula P(E OR E') = P(E) + P(E') - P(E AND E'), while for mutually exclusive events, it simplifies to P(E OR E') = P(E) + P(E') because P(E AND E') would be zero in this case.

Answer 2

The probability P(E U E') represents the chance that at least one of the events E or E' occurs, potentially including the case where both occur.

Step-by-step explanation:

The probability P(E U E') represents the likelihood that event E occurs, or event E' occurs, or both events occur. In other words, it is the probability of at least one of the two events happening. When considering two events, we need to understand that they could be independent, mutually exclusive, or neither. Mutually exclusive events cannot happen at the same time, which means P(E AND E') = 0 for mutually exclusive events. If events E and E' are independent, the occurrence of one does not affect the probability of the other occurring. Therefore, if E and E' are not mutually exclusive, the correct calculation for P(E U E') would be P(E) + P(E') - P(E AND E'), since any common outcomes between E and E' must be counted only once.