Probability Rule B
All possible outcomes must sum to 1Some outcome must occur on every trialSo the sum of the probabilities for all possible outcomes must be exactly 1
Probability Rule B, also known as the 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 represented as:
P(A or B) = P(A) + P(B) – P(A and B)
The key assumption behind this rule is that both events A and B are mutually exclusive, meaning they cannot occur at the same time. If the events are not mutually exclusive, then the probability of both events occurring simultaneously must be added instead of subtracted.
For example, let’s say we are rolling a fair six-sided die. The probability of rolling a 3 is 1/6 and the probability of rolling a 4 is also 1/6. So, the probability of rolling either a 3 or a 4 is:
P(3 or 4) = P(3) + P(4) – P(3 and 4)
= 1/6 + 1/6 – 0 (since rolling a 3 and a 4 simultaneously is impossible)
= 1/3
Therefore, the probability of rolling either a 3 or a 4 is 1/3.
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