# Adding Probabilities - Mutually Exclusive Outcomes

Reference > Mathematics > ProbabilityIf we want to know the probability of two mutually exclusive outcomes happening, we have a simple formula:

P(A or B) = P(A) + P(B)

We read this as "The probability of either A or B happening is equal to the probability of A happening, plus the probability of B happening."

Let's try an example:

**Example One**

When I roll the six-sided die, what is the probability that I will either get a one or a four?

**Solution**

These are mutually exclusive outcomes, so we can use the formula shown above:

Outcome A is getting a one, and outcome B is getting a four.

P(A or B) = P(A) + P(B) =**Example Two**

I draw a card from the deck of cards. What is the probability that it is either a king or a heart?

**Solution**

These are

*not*mutually exclusive, since a card could be both a king and a heart. Thus, we can't solve it using this formula. (We could solve it using the

**Example Three**

I randomly pick a letter from the alphabet. What is the probability that it is either a J, a K, or a vowel.

**Solution**

These are mutually exclusive events, since none of the vowels are either J or K. We'll use an extended version of our formula:

**Example Four**

I randomly pick a number between 50 and 200 inclusive. What is the probability that the number is either a two-digit odd number, or a three digit even number?

**Solution**

These are mutually exclusive events, since no number is both a two-digit number *and *a three-digit number.

P(O + E) = P(O) + P(E)

There are 151 possibilities, since we're including both 50 and 200.

The probability of getting a two-digit odd number isFor each scenario below, either solve it using the formula given here (if the outcomes are mutually exclusive), or state that the outcomes are not mutually exclusive.