Random Puzzles 

Workings

Hint
The answer is right in front of you.

Answer
Mississippi.

The diagram is actually the word 'mississippi' on its side.

Workings

Hint

Answer
23.

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%.

Workings

Hint
This is quite a common list.

Answer
T.

The first letters of playing cards in descending order of value.

Workings

Hint
Don't forget the extra 9's in 90, 91, etc.

Answer
300.

Reasoning
Start with: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 – which is 20 9's.

We then repeat this for 100, 200, 300, up to 900 – which is 200 9's.

But from 900 to 999 we have an extra 100 9's as each starts with a 9.

So the total is 300.