Conditional Probability
Conditional probability is the probability of an event occurring, given that another event has already occurred. It represents the updated probability based on the knowledge or information about the occurrence of another event.
The conditional probability of A given B is defined as follows:
If events A and B are independent, thenP(A intersection B) = P(A)*P(B)
,
and as a result, conditional probability P(A|B)=P(A)
.
Note
It makes sense to introduce a conditional probability only if P(B) is not equal to zero.
Let's look at the example.
Assume that there are 5
children in the family, and at least one is a girl. Calculate the probability that the eldest child is a boy assuming that each child can be a girl or a boy with equal probability.
Due to this assumption, we can use the classic definition of probability and calculate the corresponding probability using conditional probability.
Let event A is that the eldest child is a boy. Event B is that there is at least one girl. We can solve this task as follows:
Tudo estava claro?
Conteúdo do Curso
Probability Theory Basics
5. Covariance and Correlation
Probability Theory Basics
Conditional Probability
Conditional probability is the probability of an event occurring, given that another event has already occurred. It represents the updated probability based on the knowledge or information about the occurrence of another event.
The conditional probability of A given B is defined as follows:
If events A and B are independent, thenP(A intersection B) = P(A)*P(B)
,
and as a result, conditional probability P(A|B)=P(A)
.
Note
It makes sense to introduce a conditional probability only if P(B) is not equal to zero.
Let's look at the example.
Assume that there are 5
children in the family, and at least one is a girl. Calculate the probability that the eldest child is a boy assuming that each child can be a girl or a boy with equal probability.
Due to this assumption, we can use the classic definition of probability and calculate the corresponding probability using conditional probability.
Let event A is that the eldest child is a boy. Event B is that there is at least one girl. We can solve this task as follows:
Tudo estava claro?