What is the sum of probabilities for two mutually exclusive events?

What is the sum of probabilities for two mutually exclusive events?

• A. P(A ∩ B) = 0
• B. P(AUB) = P(A) + P(B)
• C. P(AUB) = P(A) - P(B)
• D. P(AUB) = P(A) x P(B)

Answer: (B)

The sum of probabilities for two mutually exclusive events is given by the equation P(AUB) = P(A) + P(B). This is because mutually exclusive events cannot occur at the same time; thus, the probability that either event A happens or event B happens is simply the sum of their individual probabilities. To elaborate, when two events are mutually exclusive, the occurrence of one event means that the other cannot occur at all, leading to the necessity of adding their probabilities together to find the total probability of either event occurring. For example, if event A represents rolling a die and getting a 1, and event B represents rolling a die and getting a 2, since both cannot happen simultaneously, the combined probability P(A or B) equals P(A) + P(B). If P(A) is 1/6 and P(B) is 1/6, then P(AUB) equals 1/6 + 1/6 = 1/3. The other options do not accurately reflect the relationship between mutually exclusive events. One states that the probability of both events occurring together is zero, which is true but does not provide the sum of probabilities. Another option incorrectly represents the relationship with a subtraction, and yet another suggests a

The sum of probabilities for two mutually exclusive events is given by the equation P(AUB) = P(A) + P(B). This is because mutually exclusive events cannot occur at the same time; thus, the probability that either event A happens or event B happens is simply the sum of their individual probabilities.

To elaborate, when two events are mutually exclusive, the occurrence of one event means that the other cannot occur at all, leading to the necessity of adding their probabilities together to find the total probability of either event occurring.

For example, if event A represents rolling a die and getting a 1, and event B represents rolling a die and getting a 2, since both cannot happen simultaneously, the combined probability P(A or B) equals P(A) + P(B). If P(A) is 1/6 and P(B) is 1/6, then P(AUB) equals 1/6 + 1/6 = 1/3.

The other options do not accurately reflect the relationship between mutually exclusive events. One states that the probability of both events occurring together is zero, which is true but does not provide the sum of probabilities. Another option incorrectly represents the relationship with a subtraction, and yet another suggests a