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I think I figured it out via naive reasoning. We know that they have two kids, so, marking a boy as 1 and a girl as 0, there are four options as to what they can be: 00, 01, 10 and 11. Now, we know that one is a boy, so it can't be 00. Thus, there are three options, of which only one, option 11, is what we are looking for. Thus the probability is 1/3.
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Day 3: Conditional Probability
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I think I figured it out via naive reasoning. We know that they have two kids, so, marking a boy as 1 and a girl as 0, there are four options as to what they can be: 00, 01, 10 and 11. Now, we know that one is a boy, so it can't be 00. Thus, there are three options, of which only one, option 11, is what we are looking for. Thus the probability is 1/3.