24+Mutually+Exclusive+Events

**Summary**:

Mutually exclusive events are two events that cannot happen at the same time. These events could be like drawing a red card that is also a club, this is mutually exclusive because there is no such thing as a red club because clubs are black. In a problem asking about probabilities you know that the answers is mutually exclusive because the word "or" is in the problem. So the problem would ask what is the probability that a red card or a club be picked from a deck of cards. The equation used to find the probability is: P (A or B) = P (A) + P (B) – P (A and B).

**Useful Links:**

[]

[]

[]

[]

[]

[]

**Rules, Properties, and Formulas:**

Mutually Exclusive can be best defined as two events in which the occurrence of one implies that the other shall not occur, i.e., that they cannot both occur (see diagram bellow). Mutual Exclusive problems rely on addition rather than multiplication and have the property: P (//A// ∩ //B// ) = 0. Thus, when “A” and “B” are Mutually Exclusive, the formula is: **P (A or B) = P (A) + P (B).**



**Examples:**

1) A card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a a red 7 or a black Queen?

//(Answer) Since there are only two red sevens the probability of choosing one is 2/52 or 1/26 which is the same probability as getting a black queen. Then you have to add them and you get 2/26 or 1/13. So the probability that you will get either a red 7 or a black Queen is 1/13.//

2) Is the question Mutually Exclusive if it isn't make it mutually exclusive: A 6 sided die is rolled. what is the probability that the roll will be a 5 or odd?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">(//Answer) It isn't because both can occur at the same time. To make it mutually exclusive you need to ether change the 5 to an even number or change odd to even.//

<span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">3) There are two types of fish in a fish tank 25 Goldfish, and 38 Beta Fish what is the probability that you will get 4 goldfish in a row or only getting 5 beta fish in a row?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">//(Answer) First you have to add to find how many fish are all together. which is 61 then you need to find the probability which is 4/63 and 5/63 respectively. So in order to find both you need to add and go get 9/63 which is 1/7 that will happen//