Conditional Probability of Male Bird with Blue Eyes

What is the probability that the bird is male given that it has blue eyes?

This problem involves understanding the concept of conditional probability, which is a fundamental principle in probability theory. Conditional probability provides a way to measure the likelihood of an event occurring, given that another event has occurred. This is crucial when dealing with dependent events where the occurrence of one event affects the probability of another. In this context, we want to find the probability that a bird is male given the information that it has blue eyes.

To solve this type of problem, we apply the formula for conditional probability: the probability of event A given event B is the probability of A and B occurring together divided by the probability of B. This approach requires an understanding of joint probabilities and marginal probabilities. One common method to visualize and solve these kinds of problems is using a frequency table or a Venn diagram, which helps in organizing the given data and visualizing the relationships between different events. This allows for an intuitive understanding of how the known probability (B) affects the probability of the other event (A).