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  Reasoning

Sisters & Brothers
 
Q Suppose I have two siblings, and at least one of them is a girl. What are the odds that I have two sisters? Supposing I have two siblings, and the older one is a boy. What are the odds that I have two brothers?


 
A The probability that both are girls is 1/3. (The odds that both are girls is 1 to 2- one way it can be true against two ways it can not.) There are four possibilities when considering the gender of two siblings: girl-girl, girl-boy, boy-girl, and boy-boy. Given that I have one sister, the boy-boy combination is impossible. So in this case, there are three possible combinations, and only one with both girls.

In the second case, the probability of having two brothers is 1/2. (The odds are "even" - 1 to 1.) The same four possibilities for gender must be considered. Girl- girl is not possible from the given information. The statement "the older one is a boy" also eliminates the girl-boy option. This leaves only two choices.

STRATEGY: Draw a picture or diagram.