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Understanding the Probability of Gender Combinations

Introduction to the Scenario

Dr. Johnson is a parent of two children, one of whom is a girl. In this context, we are tasked with determining the likelihood that the other child is also a girl, given that the probability of each child being either gender is ½.

Possible Combinations of Children

To analyze this situation, we can outline the potential combinations of the two children. The possible gender combinations are:

– Girl-Girl
– Girl-Boy
– Boy-Girl

Calculating the Probability

Since we are specifically interested in the scenario where both children are girls, we can see that among the three possible outcomes, only one combination (Girl-Girl) meets this criterion.

Thus, the probability that the other child is also a girl is calculated as follows:

– Total possible outcomes: 3
– Favorable outcomes (Girl-Girl): 1

Therefore, the probability is expressed as:

Probability = Favorable Outcomes / Total Outcomes = 1/3.