Explain with examples the rules of addition and multiplication in theory of
probability.
Answers
Answer:
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Step-by-step explanation:
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The rules of addition and multiplication in the theory of probability.
- Additional rule of probability:
The probabilities of event A & event B can be calculated by just adding the probability of one event A with another event B and then subtracting any intersection of the two events.
P(A or B)=P(A)+P(B)−P(A and B) which can be written as ( ∪ ) = () + () − ( ∩ )
If event A and event B are incompatible, P(AnB)=0 . Then there's a chance that one of the occurrences will happen is:
P(A or B)=P(A)+P(B)
For Example:
Q-What is the chance that a single card will be drawn from a normal deck of cards will be either an ace, or spade?
Answer-Let x be the occurrence of selecting an ace and Y be the occurance of selecting spade.
P(X)=4/52
P(Y)=13/52
The two occurance are not mutually incompatible, because there is a chance that the card will be both an ace and a spade
P(X and Y)=1/52
P(X or Y)=4/52+13/52-1/52
=16/52
=4/13
- Multiplication rule of probability:
In probability experimentation, if A & B are two individual occurrences, the chance that both events occur at a similar time is:
P(A and B)=P(A)⋅P(B)
In the case of dependent occurrances, the chance of both happening at the same time is:
P(A and B)=P(A)⋅P(B | A)
(The notation P(B | A) stands for "the probability of B if A occurs.")
For example:
Q-You have a black tie, a brown tie, and a yellow tie. You also have four shirts: blue, green, pink, white. What's the probability that you might select the yellow tie and blue shirt at random?
Answer:
Both the events that occurred are independent. The choice of the tie has no effect on shirt selection.
There are three different ties, so the probability of choosing the yellow is 1/3
There are four different shirts, so the probability of choosing the blue shirt is ¼
So, by the Multiplication Rule:
P(yellow tie, blue shirt)=⅓,¼
=1/12