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115 CFA

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115.020.30.03 Reading 8 - 3. Addition Rule for Probabilities

# 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur

## e. explain the multiplication, addition, and total probability rules;

## f. calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events.

## g. distinguish between dependent and independent events;

What is the addition rule for probabilities? What is the mathematical notation?

It is the inclusive probability that either A OR B (or both) will happen.

$$P(A or B) = P(A) + P(B) - P(AB)$$

- Subtract the `P(AB)`

because it is already counted individually in `P(A)`

and `P(B)`

and we don't want to count it twice

How would you calculate the probability of rolling a six on at least one of two throws of a 6-sided dice?

- `P(A or B) = P(A) + P(B) - P(AB)`

- `P(A or B) = 1\6 + 1\6 - (1\6 * 1\6)`

= .31

- Or use the complement method: one minus the probability of NOT getting the result you want on both rolls (usually easier)

- `P(A or B) = 1 - (5/6 * 5/6)`

= .31

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- CFA