Probability Formula
The probability formula defines the likelihood of the happening of an event. It is the ratio of favourable outcomes to the total favourable outcomes. The probability formula can be expressed as,
- P(A)= number of favourable outcomes / total number of outcomes
- Here,
- P(B) is the probability of an event 'B'.
- n(B) is several favourable outcomes of an event 'B'.
- n(S) is the total number of events occurring in the sample space.
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Formulas of different Probability
- Probability formula having summation rule: Whenever an event is the union of two other events, say A and B :
- P(A or B) =P(A) + P(B) -P(A ∩ B)
- P(A ∪ B) =P(A) + P(B) -P(A ∩ B)
Probability formula with complementing rule: Whenever event is complement of another event, specifically, if A is event, then P(not A) = 1 - P(A) or P(A') = 1 - P(A).P(A) + P(A')
Probability formula with the contingent rule: When event A is known to have occurred and the probability of the event B is desired, then P(B for given A) = P(A and B), P(A for given B) It can be vice versa in case of the event B.
P(B|A) = P(A ∩ B)/P(A)
Probability formula with the multiplication rule: Whenever an event is the intersection of two other events i.e (events A and B) need to occur at the same time. Then
P(A and B) = P(A).P(B).P(A ∩ B) = P(A).P(B|A)
Solved example of Probability Formula
Example 1: Find the probability of getting a number less than 5 when a dice is rolled by using the probability formula.
- Solution :
- To find:
- Probability of getting a number less than 5
- Given: Sample space = {1,2,3,4,5,6}
- Getting a number less than 5 = {1,2,3,4}
- Therefore, n(S) = 6
- n(A) = 4
- Using the Probability Formula,
- P(A) = (n(A)/(n(s)))
- P(A) = 4/6
- m = 2/3
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