Understanding the Probability of Events A or B | Mutually Exclusive and Non-Mutually Exclusive Scenarios

P(A or B)

In probability theory, P(A or B) represents the probability that event A or event B occurs

In probability theory, P(A or B) represents the probability that event A or event B occurs.

The formula to calculate P(A or B) depends on whether the events A and B are mutually exclusive or not.

1. If events A and B are mutually exclusive, it means that they cannot occur at the same time. In this case, the formula to calculate P(A or B) is:
P(A or B) = P(A) + P(B)

For example, if you wanted to calculate the probability of flipping a coin and getting heads or tails, since heads and tails are mutually exclusive events, the probability would be:
P(Heads or Tails) = P(Heads) + P(Tails) = 1/2 + 1/2 = 1

2. If events A and B are not mutually exclusive, it means that they can occur at the same time. In this case, the formula to calculate P(A or B) is:
P(A or B) = P(A) + P(B) – P(A and B)

For example, if you wanted to calculate the probability of rolling a die and getting an even number or a number less than 4, the probability would be:
P(Even or Less than 4) = P(Even) + P(Less than 4) – P(Even and Less than 4) = 3/6 + 3/6 – 2/6 = 4/6 = 2/3

Here, P(Even and Less than 4) represents the probability of rolling a number that is both even and less than 4, which is 2 out of 6 possible outcomes (2, 4, 6).

Remember, when calculating probabilities, the sum of all possible outcomes should always equal 1.

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