Addition Law For Mutually Exclusive Events

First go through the mutually exclusive events. These are the two or more than two events that have nothing in common. Theorem for Addition law of mutually exclusive events states that:

If there are two events say “x” and “y” and both are mutually exclusive events, then the probability that either “x” or “y” occur is the sum of the probabilities of both the events.

Suppose there are two events named as “x” and “y”, both events have nothing in common. Addition of such event is done by following the addition law for mutually exclusive events.

P(x or y) = p(x u y) = p(x) + p(y)

Let make it clear by solving simple examples.

Addition Law For Mutually Exclusive Events Examples:

Example 1:

A single card is selected from a deck of 52 cards. Find the probability that the randomly selected card is either king or queen.

Solution:

Total number of outcomes = 52

Probability of each single card = 1/52

Now let first find the probability of queen

Probability of queen is represented by = P(Q)

There are four queens in a deck of playing cards.

Therefore, probability of queen = P(Q) = 4/52

Now, let find the probability of king

Probability of king is represented by = P(k)

In the same manner there are four kings in a deck of 52 playing cards.

Therefore, probability of queen = P(K) = 4/52

Addition law of mutually exclusive event is used, as the requirement is to find the probability of king or queen.

Therefore,

P(K or Q) = P(K u Q) = P(K) + P(Q) = 4/52 + 4/52 = 8/52

Example 2:

A dice is thrown. Find the probability that the face is less than three or it is multiple of 5.

Solution:

When a dice is rolled, there are six possible outcomes

Sample space = S = {1, 2, 3, 4, 5, 6}

Let first find the probability of face that are less than 3.

A = {1, 2} = 2/6

Now second part is that the face is multiple of 5.

B = {5} = 1/6

Use addition law, as again there is nothing in common between the two events.

P (A or B) = P(A u B) = P(A) + P(B) = {1, 2} + {5} = {1, 2, 5}

P(A or B) = 2/6 + 1/6 = 1/2