Solve this Riddle if you can

Edit: that got me all confused now.

It's a bit hard to explain this, but it's not about the order of the children, it's about probabilities.

Because they didn't have to rewind the tape?

Another explanation is:

When you know that there are two children in a family, then you can have four situations:

2 girls, a boy and a girl, a girl and a boy and two boys.

Now you know that there is at least one boy. Hence, the first option is not valid. What is the chance it are two boys? 1/3.

If the question would have been 'what is the chance that the other child is a boy?' then would the chance be a 1/2, because the gender of a child is unrelated to the gender of other children in the family.

Concerning the dead man: if the man would have commited suicide, then could he not rewind the tape to the moment prior to the gun shot. The tape would have run to the end and still be running when the police entered the room.

Right, that was quick.

A car drove from point A to point B doing 40 miles per hour. It then drove back from point B to point A doing 80 miles per hour.

Was the average speed equal to, greater than or lesser than 60 miles per hour?

less

Or better yet, what are the chances of a coin landing heads 20 times in a row if it just landed tails 20 times in a row.

Indeed.

However there is one explanation which really helps grasp the reasoning behind it (it was already mentioned here in the thread somewhere).

Imagine if instead of three doors, there are a million doors. Only one has a car behind it, the other 999,999 have goats. You are asked to choose one and you do. Your chances of choosing the right door is one in a million. Next, the host opens 999,998 doors which have goats behind them, leaving only the door you chose and another door. Behind one of these doors there's a car.

Now, do you really believe the door you chose has a car behind it? 

Try to explain it this way to people. It usually does the trick.

Yes of course, that was my point. Just another way to say it to try and confuse people who are really bad at math / common sense.

True.

A man jumps from a 20 story building and falls all the way to the ground. But afterwards he didn't feel any pain. How?

There are two answers.

1. You don't feel anything anymore the moment you have hit the ground.

2. He was already dead the moment he started to fall. This one is wrong, because dead men can't jump. He can die during the fall, that is.

An old man hobbles into the war-claims office and requests compensation for injuries suffered while fighting during the first world war. He produces an old and dusty letter which reads: "I hereby declare that Angus Smith fought gallantly in the first world war under my command and sustained severe injuries in battle. -General Arthur E. Aiken, November 1921." The secretary takes one look at the letter and declares it to be fake. How did she know?

I guess the other answer might be that he had a parachute.

A valid try, but he didn't (I think the fact that he "fell" all the way to the ground implies so).

True, he could have simply died from the fall (or in the middle of the fall from a heart attack, thanks Loek for that creative thought), therefore feel no pain afterwards.

What is the second solution?

That is a good one Piecefodder. Or the building is a miniature building, actually only half a meter high. Now do we have already four answers.

He jumped from the second storey of the building.

At first I thought it was the date, but he could have wrote the letter after the war has already ended.

But of course, in 1921 the great war was not called the "first world war" yet 

Yes that's true, he jumped from the first storey. I guess you could say that warrants some pain, but it's really not that high, and let's say he was a strong fella. And maybe the ground was soft-ish too