Here are the three examples (for this time around) of areas in mathematics where ‘the truth’ isn’t quite so obvious:
1. Four Child Families Interestingly enough, the chances that a four-child family will end up with 2 boys & 2 girls is NOT “50-50”. It’s actually 6 out of 16 (or 3/8) – a little less than half. You can see this by listing all SIXTEEN possibilities, and noting that only SIX are 2B & 2G. (To see this illustrated, visit Four Child Family.) You’ll also see that it’s actually more likely to get 3 children of one sex and 1 of the other – that outcome is actually 50-50 (8 of 16). (This is also illustrated in the link above.)
2. GREAT “bar bet” ! Are you ready for this? 🙂 It turns out that if you’re in a room of more than 23 people, the chances of there being duplicate birthdays (month/day, not year) in the group is actually better than half (50-50) !! By the time you get to 30 or 35 people it’s up in the 70% likely stage! This is DEFINITELY hard to believe, but it’s true. Try it yourself!! You’ll lose frequently, yes, but you’ll win more than you lose. (The math here is more obtuse, but if you’d like to see it, let me know.)
NOTE: Here’s part of the ‘problem’. , I did NOT say that 2 folks will share a GIVEN birthday, picked ahead of time (like June 28 or your birthday) . . . that is nowhere near as likely! We’re only saying that there will be a set of duplicate birthdays for some date.
3. Caveat Emptor! Have you ever noticed that carpet is often priced by the square foot, rather than the square yard? There is a (possibly devious? 🙂 ) reason for this. That’s because it’s easy for us consumers to make a careless mistake here. Think carefully: There are NINE (not THREE!) square feet in a square yard. (Visualize a 3 x 3 block, a yard on each side. It takes 9 sq. ft. blocks to fill it, not 3.) SO, let’s say the carpet is priced at $1/sq. ft. The retailer wouldn’t mind at all if you think that means $3 sq. yd, when in fact, it actually translates $9 sq. yd. ! Beware!
(If I just saved you some money on a carpet purchase, I’ll be happy to accept 50% of the difference. :-))
The counter-intuitive example that comes to mind for me deals with percents. In the stock market, if you buy and stock for $50 and it goes up to $75 you make 50%. But when the stock goes back down to $50, you only lose 33%. Brokers love to use this one to their advantage. So, one year you make 50%, the next you lose 33% and you think you’re doing pretty good.
Ah, yes!! This is a MARVELOUS example!! And one of my favorites, as well . . . not sure how I missed it when I wrote that. Time for a counterintuitive #2!!