Final answer:
The conditional probability P(A|C) is the probability of event A occurring given that event C has occurred. To find P(A|C), calculate the probability of event A using the reduced sample space C. For example, if we have ethnic groups with different blood types, we can find the probability of selecting blood type A from among those who belong to ethnic group 3.
Step-by-step explanation:
The conditional probability P(A|B) is the probability of event A occurring given that event B has occurred. In this case, we want to find the probability of event A occurring given that event C has occurred, which can be represented as P(A|C).
To find P(A|C), we need to calculate the probability of event A using the reduced sample space C. Event C is defined as selecting ethnic group 3, while Event A is defined as selecting blood type A. We need to find the probability of selecting blood type A from among those who belong to ethnic group 3.
For example, if we have the following data:
- Ethnic group 1 has blood type A and B
- Ethnic group 2 has blood type B
- Ethnic group 3 has blood type A, B, and AB
- Ethnic group 4 has blood type O
Then, the reduced sample space C would be: {1, 2, 3}
And the reduced sample space A given C would be: {1, 3}
To find P(A|C), we calculate the probability as follows:
P(A|C) = (number of outcomes in A given C) / (number of outcomes in C)
P(A|C) = (number of outcomes in {1, 3}) / (number of outcomes in {1, 2, 3})
In this case, the probability of event A occurring given that event C has occurred can be calculated by counting the number of individuals who belong to ethnic group 3 and have blood type A, and dividing that by the total number of individuals who belong to ethnic group 3.