# #69 More probability questions – correction

I often tell my students that I make mistakes in class on purpose as a teaching strategy, to encourage them to pay close attention, check my work regularly rather than simply copy what I say into their notes, and speak up when they notice something that they question.

This is partially true, but most of the mistakes that I make in class are, of course, genuine ones rather than purposeful. I admit that I sometimes try to bluff my way through, with tongue firmly planted in cheek, claiming that my mistake had been intentional, an application of that teaching strategy.

Thanks very much to the careful blog reader who spotted a mistake of mine in today’s post. In a follow-up discussion to the first example, I wrote: *If the marginal percentages had been 28% and 43%, then the largest possible value for the intersection percentage would have been 28% + 43% = 71%.* This is not true, because the intersection percentage can never exceed either of the marginal percentages. With marginal percentages of 28% and 43%, the largest possible value for the intersection percentage would be 28%.

Perhaps I was thinking of the largest possible percentage for the *union* of the two events, which would indeed be 28% + 43% = 71%. Or perhaps I was not thinking much at all when I wrote that sentence. Or perhaps, just possibly, you might be so kind as to entertain the notion that I made this mistake on purpose, as an example of a teaching strategy, which I am now drawing to your attention?