You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles, and 2 empty bowls. He then says, 'Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die.'

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

I know a ten-letter word in the English language which can be typed using only the top rows of the computer keyboard.

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?

What is more useful when it is broken?

In a box, there is a jumble of 7 red balls, 6 blue balls, 5 green balls, and 4 yellow balls. What is the minimum number of balls, will you have to pick up so that you have at least 4 balls of the same colour?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?