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In order to use Venn diagrams when talking about events, we must first understand the term 'mutually exclusive'. Imagine there are two events: event A and event B. If they both cannot happen at the same time then A and B are mutually exclusive.
Example
Venn Diagrams for Sets Added Aug 1, 2010 by Poodiack in Mathematics Enter an expression like (A Union B) Intersect (Complement C) to describe a combination of two or three sets and get the notation and Venn diagram. Calculator to create venn diagram for two sets.The Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common. It is the pictorial representations of sets represented by closed figures are called set diagrams or Venn diagrams.
Jim is going to roll a dice.
Let’s say that event A is rolling an odd number and event B is rolling the number 2. Quite clearly these events are mutually exclusive because you cannot roll both a 2 and an odd number with a single roll of a dice.
This is represented on a Venn diagram like this:
The fact that the two circles do not overlap shows that the two events are mutually exclusive.
This means that the probability of A or B happening = the probability of A + the probability of B.
This is written as P(A or B) = P(A) + P(B).
Consider a second example where event A is chosen to be getting an even number and event B is chosen to be getting a number greater than 3. These events are not mutually exclusive because the criteria for both is fulfilled if we roll a 4 or a 6.
The 4 and 6 are placed in the overlapping middle quadrant as they represent outcomes which satisfy both events.
This means that the probability of A or B happening = the probability of A + the probability of B – the probability of A and B.
P(A or B) = P(A) + P(B) – P(A and B).
Let’s see if this is correct:
P(A or B) means the probability of getting an even number or a number greater than 3. This means we succeed if we get {2,4,6} or {4,5,6}, so in other words we succeed if we get {2,4,5,6}.
The probability of this is .
P(A) means the probability of getting an even number. This means we succeed if we get a {2,4,6}, so the probability is .
P(B) means the probability of getting a number greater than three. This means we succeed if we get {4,5,6}, so the probability of this is also .
P(A and B) means the probability of getting an even number that is also greater than 3. This means we succeed if we get {4,6}, so the probability is .
. So the formula works.
In the previous section, we used the notation P(A and B) which is called A intersection B. The outcomes which satisfy both event A and event B, this is written P(A ∩ B) and is the overlapping area on the Venn diagram.
We also used the notation P(A or B) which is called A union B, the outcomes which satisfy either event A or event B, this is written as:
P(A ∪ B)
It's represented by the two circles including the overlapping section on the Venn diagram.
It is important to note that all the outcomes that do not satisfy event a are written as A’. This is said to be the complement of A, and is represented by all the area outside of circle A on the Venn diagram.
A bag contains 4 green balls, 3 red balls and 7 balls of other colours. Draw a Venn diagram for this information.
Draw a Venn diagram for the outcome of a rugby match where event A is that the home side scores a try and event B is that the home side wins the match.
Notice that these events are not mutually exclusive because you can score a try and win a match. In fact, it’s quite common. However, it is also possible to score a try and still lose. It is also possible to win without scoring any tries.
In order to use Venn diagrams when talking about events, we must first understand the term 'mutually exclusive'. Imagine there are two events: event A and event B. If they both cannot happen at the same time then A and B are mutually exclusive.
Example
Jim is going to roll a dice.
Let’s say that event A is rolling an odd number and event B is rolling the number 2. Quite clearly these events are mutually exclusive because you cannot roll both a 2 and an odd number with a single roll of a dice.
This is represented on a Venn diagram like this:
The fact that the two circles do not overlap shows that the two events are mutually exclusive.
This means that the probability of A or B happening = the probability of A + the probability of B.
This is written as P(A or B) = P(A) + P(B).
Consider a second example where event A is chosen to be getting an even number and event B is chosen to be getting a number greater than 3. These events are not mutually exclusive because the criteria for both is fulfilled if we roll a 4 or a 6.
The 4 and 6 are placed in the overlapping middle quadrant as they represent outcomes which satisfy both events.
This means that the probability of A or B happening = the probability of A + the probability of B – the probability of A and B.
P(A or B) = P(A) + P(B) – P(A and B).
Let’s see if this is correct:
P(A or B) means the probability of getting an even number or a number greater than 3. This means we succeed if we get {2,4,6} or {4,5,6}, so in other words we succeed if we get {2,4,5,6}.
The probability of this is .
P(A) means the probability of getting an even number. This means we succeed if we get a {2,4,6}, so the probability is .
P(B) means the probability of getting a number greater than three. This means we succeed if we get {4,5,6}, so the probability of this is also .
P(A and B) means the probability of getting an even number that is also greater than 3. This means we succeed if we get {4,6}, so the probability is .
. So the formula works.
In the previous section, we used the notation P(A and B) which is called A intersection B. The outcomes which satisfy both event A and event B, this is written P(A ∩ B) and is the overlapping area on the Venn diagram.
We also used the notation P(A or B) which is called A union B, the outcomes which satisfy either event A or event B, this is written as:
P(A ∪ B)
It's represented by the two circles including the overlapping section on the Venn diagram.
It is important to note that all the outcomes that do not satisfy event a are written as A’. This is said to be the complement of A, and is represented by all the area outside of circle A on the Venn diagram.
A bag contains 4 green balls, 3 red balls and 7 balls of other colours. Draw a Venn diagram for this information.
Draw a Venn diagram for the outcome of a rugby match where event A is that the home side scores a try and event B is that the home side wins the match.
Notice that these events are not mutually exclusive because you can score a try and win a match. In fact, it’s quite common. However, it is also possible to score a try and still lose. It is also possible to win without scoring any tries.