Crostic Mathematics Level 5 answers
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Mathematics Level 5
In a crowded room, two people probably share a birthday. In a room of 23 people there’s a 50% chance that two people have the same birthday. With 75 people the chances rise to 99 per cent! The birthday paradox is strange, counter-intuitive, and completely true. It's only a "paradox" because our brains can't handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we're involved in (both faulty assumptions, by the way). We could list the pairs and count all the ways they could match. But that’s hard: there could be 1, 2, 3 or even 23 matches! It's like asking "What's the chance of getting one or more heads in 23 coin flips?" There are so many possibilities: heads on the first throw, or the 3rd, or the last, or the 1st and 3rd, the 2nd and 21st, and so on. How do we solve the coin problem? Flip it around. Rather than counting every way to get heads, find the chance of getting all tails, our "problem scenario". If there’s a 1% chance of getting all tails, there’s a 99% chance of having at least one head. If we subtract the chance of a problem scenario from 1 we are left with the probability of a good scenario. The same principle applies for birthdays. Instead of finding all the ways we match, find the chance that everyone is different, the "problem scenario". We then take the opposite probability and get the chance of a match. Two people have the same birthday
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Mathematics Answers