what's the probability of getting a king or a queen from a pack of 52 cards?

What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

You are trapped into a death trap by the famous jigsaw killer. As usual, a screen flashes in front of you and explains you the trap game. There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die. How will divide the pearls to increase your chances of survival?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?