Question

What is the addition rule of probability?

Accepted Answer

The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening.

Mathematically, If $A$ and $B$ are two mutually exclusive events. Then the probability that either one of the events will occur is

$P (A U B) = P (A) + P (B)$

If $A$ and $B$ are two events in a probability experiment, then the probability that either one of the events will occur is:

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

For Example: If you take out a single card from a regular pack of cards, what is the probability that the card is either an ace or spade?

Let $X$ be the event of picking an ace and $Y$ be the event of picking a spade.

$P (X) = \frac{4}{52}$ , $P (Y) = \frac{13}{52},$ and $P (X \cap Y) = \frac{1}{52}$

Thus, $P (X or Y) = P (X) + P (Y) - P (X \cap Y)$

$= \frac{4}{52} + \frac{13}{52} - \frac{1}{52}$

$= \frac{16}{52}$

$= \frac{4}{13}$ which is the required answer.

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Probabilities of combined events

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Probabilities of combined events

Questions from Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Probabilities of combined events with Hints & Solutions

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