Understanding the General Addition Rule for Two Events | Probability of Union Calculation

General Addition Rule for Two Events

The General Addition Rule for Two Events is a fundamental concept in probability theory that allows us to calculate the probability of the union of two events occurring

The General Addition Rule for Two Events is a fundamental concept in probability theory that allows us to calculate the probability of the union of two events occurring.

Let’s consider two events A and B. The General Addition Rule states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities, minus the probability of both events occurring simultaneously. Mathematically, it can be expressed as:

P(A or B) = P(A) + P(B) – P(A and B)

Here, P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A and B) represents the probability of both events A and B occurring simultaneously.

To better understand this rule, let’s consider an example. Suppose we have a bag of marbles containing 5 red marbles and 7 blue marbles. We randomly select a marble from the bag. Let event A represent selecting a red marble, and event B represent selecting a blue marble.

The probability of event A occurring (P(A)) is 5/12, since there are 5 red marbles out of a total of 12 marbles.

The probability of event B occurring (P(B)) is 7/12, since there are 7 blue marbles out of a total of 12 marbles.

Now, let’s calculate the probability of either event A or event B occurring (P(A or B)). According to the General Addition Rule:

P(A or B) = P(A) + P(B) – P(A and B)

Since selecting a red marble and selecting a blue marble are mutually exclusive events (they cannot happen at the same time), P(A and B) = 0.

Therefore, P(A or B) = P(A) + P(B) – P(A and B) = 5/12 + 7/12 – 0 = 12/12 = 1.

So, in this example, the probability of either selecting a red marble or selecting a blue marble is 1, or 100%.

The General Addition Rule for Two Events allows us to calculate the probability of the union of two events occurring, taking into account the possibility of both events occurring simultaneously. It is a useful tool in probability theory and has wide applications in various fields such as statistics, economics, and decision-making.

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