How many words can a pen with half refill write?

What can you catch but never throw?

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?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

I am white when I am dirty, and black when I am clean. What am I?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

In the four images below, can you find the odd one out?

My thunder comes before the lightning; my lightning comes before clouds; my rain dries all the land it touches. What am I?

I look flat, but I am deep. Hidden realms I shelter. Lives I take, but the food I offer. At times I am beautiful. I can be calm, angry, and turbulent. I have no heart but offer pleasure as well as death. No man can own me, yet I encompass what all men must have. What am I?