The Addition Rule Using Mutually and Non-Mutually Exclusive Events For example, in a deck of cards there are

52 cards. Question number one asks, what is the

probability of selecting a king or a queen from a deck of cards; and question number two asks, what is the probability of

selecting a king or a club from a deck of cards. Question number one asks, what is the probability of selecting a king

or a queen from a deck of cards. Since we are trying to find the

probability of A or B, we are going to use the Addition Rule. Recall, there are two formulas for the

Addition Rule. For the probability of A or B, we can have the probability of A plus the probability of B. This rule

is used for mutually exclusive events. Recall that two events are considered mutually exclusive

if they do not have any simple events in common. The second formula we are going to use which is the probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B. This formula is used for non-

mutually exclusive events. So for our first example, we are going to

use the first formula because they’re not any cards in

common between a king and a queen in a deck of

cards. For example one, we’ll ultimately have the probability of a

A or B is equal to the probability of A, which is 4 out

of 52, plus the probability of B, which is

4 out of 52. Again, you have four kings and four queens in a deck of cards. Thus, we have 8 out of 52. and that reduces to 2 over 13. The second question asks, what is the probability of selecting a king or a club from a deck of cards. Once again, we are trying to find the

probability of A or B. For this example, the events are not mutually exclusive because both share a king of clubs. Therefore,

we are going to use the second formula for non-mutually exclusive events. So to find the probability of A or B using the second formula, we

find the probability of A, which is 4 out of 52, plus the probability of B, which is 13 out of 52 (because we have 13 clubs in a deck), minus the overlap of 1 out of 52. Recall that we’re subtracting out

the overlap because in probability things cannot be counted twice. The king of clubs was computed in the first probability and it was

also computed in the second probability. So by subtracting out the overlap we’re

able to only count the king of clubs once. One out of 52 is the card that they

have in common. Once we simplify, we obtain 16 out of 52 which reduces to 4 over 13.

Your Stat Class’ Featured Video of the Week:

The Addition Rule of Probability Using CardsTHANK YOU SO MUCH

Can you make an another example of addition rule of probability.. that has some divisible?? I really like your video plz make an another examples! I really need it for my test this week