Year 10 Interactive Maths - Second Edition
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A and B are said to be mutually exclusive events if they do not overlap. This means that A and B are mutually exclusive events such that if A occurs then B is excluded or if B occurs then A is excluded. That is, A and B cannot occur together. Note:Mutually exclusive events have no sample points in common.
Consider the experiment of throwing a die.
Let A be the event that an odd number is obtained and B be the event that an even number is obtained. Then: That is, A and B have no elements (sample points) in common. Hence A and B are mutually exclusive events, as shown in the following Venn
diagram.
Addition Law of Probabilities
For the example under consideration:
Note:
In general:
Consider the
experiment of throwing a die. As usual:
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Let the events be defined as follows: A = the event that an even number is obtained; and
B = the event that a prime number is obtained.
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We notice that: From (1) and (2), we obtain:
This is called the addition law of probabilities.
Example 6
Solution:
Key Termsmutually exclusive events,
addition law of probabilities
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What is P AUB if A and B are mutually exclusive?
If two events, A and B are mutually exclusive then, P(A U B) = P(A) + P(B). This follows immediately from (3). Since A and B are mutually exclusive, n(A ∩ B)=0 and so P(A ∩ B)=0.
When the two events A and B are mutually exclusive then?
Mutually Exclusive Events
If two events are disjoint, then the probability of them both occurring at the same time is 0. If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
What does it mean when a and b are mutually exclusive?
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.
What does AUB represent in P AUB?
The symbol "∪" (union) means "or". i.e., P(A∪B) is the probability of happening of the event A or B. To find, P(A∪B), we have to count the sample points that are present in both A and B. So is P(A∪B) = P(A) + P(B)?