Addition Law of Probability: The addition law of probability states that the probability of an event occurring is equal to the sum of the probabilities of t...
Addition Law of Probability:
The addition law of probability states that the probability of an event occurring is equal to the sum of the probabilities of the event occurring in each disjoint (non-overlapping) subset of the original event. In other words, P(A) = P(A ∪ B) + P(A ∩ B), where A and B are disjoint events.
Multiplication Law of Probability:
The multiplication law of probability states that the probability of an event occurring is equal to the product of the probabilities of the event occurring in each independent subset of the original event. In other words, P(A) = P(A ∩ B) × P(A ∩ C), where A, B, and C are disjoint events.
Examples:
If you roll a fair die, the probability of rolling a 1 is 1/6, and the probability of rolling a 6 is also 1/6. According to the addition law of probability, the probability of rolling a 1 or a 6 is 1/6 + 1/6 = 1.
If you have two independent events, A and B, then the probability of A occurring is independent of the probability of B occurring. According to the multiplication law of probability, the probability of A and B occurring is equal to the product of the probabilities of A and B occurring separately.
These laws are important concepts in probability theory and are used to solve a wide range of problems involving events and outcomes