Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).
Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the %age is greater than 50%.
When we have 23 people the %age is 50.729%.
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Puzzle 3
Focus on this conundrum, do it quickly, or do it slowly. What is so wrong with it? Or so right? It is a most odd conundrum. A quick brown fox jumps, hops, and vaults past a lazy dog! Can you work out what it is? Don't skip any words, and you'll soon spot it. It isn't too hard!
Answer
The entire conundrum does not have the letter E.
However, it does contain every other letter.
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Puzzle 4
Can you find the country hidden in the following sentence:
If a Dalmatian dog can catch five balls in five minutes, four balls in four minutes, and three balls in three minutes, can a Dalmatian dog catch two balls in two minutes?
If a Dalmatian dog can catch five balls in five minutes, four balls in four minutes, and three balls in three minutes, CAN A DAlmatian dog catch two balls in two minutes?
